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{"sheet":"Bernoulli","index":0,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,0,0,5],[4,6,4,9],[13,6,13,8],[8,6,8,8],[9,6,9,8],[10,6,10,8],[11,6,11,8]]}
["UNIVARIATE BERNOULLI"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Bernoulli\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"IF($B4<=$H$7,1,0)","v":1},{"$f":"bernoulli($H$7,$B4)","v":1},{"$f":"bernoulli($H$7)","v":1}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"IF($B5<=$H$7,1,0)","v":1},{"$f":"bernoulli($H$7,$B5)","v":1},1,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0,0,1,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,1,1,1,null,"prob = ",0.8,"Location","Any real number between 0 and 1, inclusive"]
[5,0.86717342695468203,0,0,0]
[6,0.27994300504477809,1,1,1,null,"Distribution Type:",null,null,"Discrete"]
[7,0.93667220783619842,0,0,1,null,"Distrbution Name:",null,null,"Bernoulli"]
[8,0.43191155671140469,1,1,1,null,"Variate Number:",null,null,"Univariate"]
[9,0.96203701528155405,0,0,0,null,"Simulation Method:",null,null,"Pseudo-Inverse Transform"]
[10,0.14240354575933512,1,1,1]
[11,0.20171971836271319,1,1,0,null,"Macro Format:",null,null,"=Bernoulli(prob, [unif])"]
[12,0.58041618261550787,1,1,1]
[13,0.34366851316718994,1,1,1,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[14,0.9651686825697714,0,0,1,null,null,null,null,"your own uniform random variable (unif). If"]
[15,0.38704808829902526,1,1,1,null,null,null,null,"not provided, the function will generate one"]
[16,0.86385756571325945,0,0,0,null,null,null,null,"to be used in the formula."]
[17,0.17476282037902591,1,1,1]
[18,0.38117659587117037,1,1,0,null,null,null,null,"2. Column C shows the formula used in the"]
[19,0.87794506028866293,0,0,1,null,null,null,null,"macro directly in the cell.  Column D generates"]
[20,0.18238019015349183,1,1,1,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,1,1,1,null,null,null,null,"same uniform random variable (column A) as"]
[22,0.74199757940000399,1,1,1,null,null,null,null,"used in Column C, and therefore the output of"]
[23,0.57082894586967958,1,1,0,null,null,null,null,"Columns C and D will match.  Column E runs"]
[24,0.90195869363590486,0,0,1,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,1,1,1,null,null,null,null,"uniform random input."]
[26,0.3929492390413114,1,1,1]
[27,0.2515715048326993,1,1,1]
[28,0.30550021398012439,1,1,1]
[29,7.9387447484473794E-2,1,1,1]
[30,0.82057811417206794,0,0,1]
[31,5.0767455327721533E-3,1,1,0]
[32,2.9980457362279278E-2,1,1,1]
[33,0.89698739215075429,0,0,1]
[34,4.8518018441997213E-2,1,1,1]
[35,0.37123916516677757,1,1,0]
[36,0.18273885825049341,1,1,0]
[37,0.12050005291704391,1,1,1]
[38,0.64945693361731327,1,1,0]
[39,0.84523354850406707,0,0,1]
[40,0.96559113278394504,0,0,1]
[41,0.66499232931154673,1,1,1]
[42,0.48716817186481609,1,1,1]
[43,0.77210315614728597,1,1,1]
[44,0.82636627627465631,0,0,0]
[45,0.30996283637913491,1,1,1]
[46,0.1840653161997976,1,1,1]
[47,0.58275788798882977,1,1,1]
[48,0.3211056530871087,1,1,1]
[49,0.94059973373021577,0,0,1]
[50,0.14907620621989892,1,1,1]
[51,0.38302044178353878,1,1,1]
[52,8.4815952479745493E-2,1,1,1]
[53,0.84221407414122895,0,0,1]
[54,0.40498559499715014,1,1,1]
[55,0.31192254229901473,1,1,1]
[56,7.3945219604894419E-2,1,1,1]
[57,0.41540561914582874,1,1,0]
[58,0.94334481547755944,0,0,1]
[59,0.6294690698059815,1,1,1]
[60,0.21751765244325438,1,1,1]
[61,0.81132182231923589,0,0,0]
[62,0.47641953418452843,1,1,1]
[63,0.92308615531225435,0,0,1]
[64,0.62241658364570296,1,1,1]
[65,0.56290274788396399,1,1,1]
[66,0.27617460253729631,{"$f":"IF($B69<=$H$7,1,0)","v":1},{"$f":"bernoulli($H$7,$B69)","v":1},{"$f":"bernoulli($H$7)","v":0}]
[{"$f":"A69+1","v":67},0.98183097898545246,0,0,0]
[68,0.17855864253016906,1,1,1]
[69,0.14106716857892998,1,1,1]
[70,0.78799892820694739,1,1,0]
[71,0.62019869479720879,1,1,1]
[72,0.32070616340267466,1,1,1]
[73,0.71916827005391148,1,1,1]
[74,0.70290736382840724,1,1,1]
[75,0.154172834186179,1,1,1]
[76,0.27977295388613965,1,1,1]
[77,0.42321062277449939,1,1,1]
[78,0.98136142771892321,0,0,1]
[79,0.20085756040090119,1,1,1]
[80,0.16133779816984994,1,1,1]
[81,0.25863578352871763,1,1,1]
[82,0.8347220398143228,0,0,1]
[83,0.51591167107959424,1,1,1]
[84,0.24633192212221666,1,1,1]
[85,0.59063871388364364,1,1,1]
[86,0.65393134749071002,1,1,1]
[87,0.56445460206933995,1,1,1]
[88,0.10565266639072934,1,1,1]
[89,0.59226465879030998,1,1,0]
[90,0.72089126375496948,1,1,1]
[91,0.58803803186325454,1,1,1]
[92,0.76602838211191659,1,1,0]
[93,0.48285856602942256,1,1,1]
[94,0.62864718503333628,1,1,1]
[95,0.33779794281158637,1,1,0]
[96,0.47576831339143399,1,1,1]
[97,5.6312473117793416E-2,1,1,1]
[98,0.80804733641082538,0,0,1]
[99,0.49894266970018275,1,1,1]
[100,0.32081795804802316,1,1,1]

{"sheet":"Beta","index":1,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,4,14,6],[0,0,0,4],[4,4,4,7],[9,4,9,6],[10,4,10,6],[11,4,11,6],[12,4,12,6]]}
["UNIVARIATE BETA"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"beta($F$7,$F$8)","v":0.21845975655208694}]
[{"$f":"A4+1","v":2},0.23638045377472242,null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.41493032535065161,null,null,"Name","Value","Type","Feasible Range"]
[4,0.27536928231433599,null,null,"alpha1 = ",2,"Shape","Any Finite Positive Real Number"]
[{"$f":"A7+1","v":5},0.18941180363532747,null,null,"alpha2 = ",5,"Shape","Any Finite Positive Real Number"]
[6,0.32885195055563599]
[7,0.31980175493724988,null,null,"Distribution Type:",null,null,"Continuous"]
[8,0.17899809902004626,null,null,"Distrbution Name:",null,null,"Beta"]
[9,0.21956240910072064,null,null,"Variate Number:",null,null,"Univariate"]
[10,0.19648813568395712,null,null,"Simulation Method:",null,null,"Convolution"]
[11,0.40851577875577566]
[12,0.28013792734443294,null,null,"Macro Format:",null,null,"=Beta(alpha1, alpha2)"]
[13,3.5318314354919292E-2]
[14,0.43262833635721937]
[15,0.37918712923877035]
[16,0.43456068297928474,null,null,null,null,"Notes:","1. The Beta distribution does not lend"]
[17,0.3810035489682706,null,null,null,null,null,"itself easily to a manual presentation so no"]
[18,8.8227370488167658E-2,null,null,null,null,null,"manual example is provided here, only the"]
[19,0.22346908548491332,null,null,null,null,null,"output of the macro generated variates."]
[20,0.66944355126614907]
[21,0.13219993050133796]
[22,0.174250837310159]
[23,0.41961227304428578]
[24,0.11393890231367841]
[25,0.3725558932430611]
[26,4.9321456951959858E-2]
[27,6.31161337516251E-2]
[28,0.23206678485434837]
[29,0.44178268702085982]
[30,0.21493022280866]
[31,0.20781636200178863]
[32,0.23810956981977627]
[33,{"$f":"beta($F$7,$F$8)","v":0.34166989811742238}]
[34,0.32103755757867003]
[35,7.841903241738872E-2]
[36,7.157718534716688E-3]
[{"$f":"A39+1","v":37},0.5944739231324514]
[38,0.25662388208273768]
[39,0.11754409864213303]
[40,0.15572598358102921]
[41,0.18691320984143689]
[42,0.35730346981700989]
[43,0.65802155899583803]
[44,0.59600862378004438]
[45,0.65994594740963053]
[46,0.18232547217995199]
[47,0.28774748510183368]
[48,7.2777904122873438E-2]
[49,0.43611118328000725]
[50,0.24234753579942139]
[51,0.19696963118591471]
[52,0.58533957264864167]
[53,0.13608515011220787]
[54,0.24400510914737766]
[55,0.25740811943600583]
[56,0.45404733610353676]
[57,0.64164630019152058]
[58,0.23677754540267956]
[59,0.54753721092014229]
[60,0.35521540154524944]
[61,0.71851695710368046]
[62,0.32573025643558678]
[63,0.13740886666737195]
[64,0.19923314017931909]
[65,{"$f":"beta($F$7,$F$8)","v":0.26093414842618551}]
[66,0.36219797094077572]
[{"$f":"A69+1","v":67},0.24925283637652729]
[68,0.21439777620960557]
[69,0.24252962675179643]
[70,0.12574580431393093]
[71,0.34799971976774741]
[72,0.22108185059459864]
[73,0.30176109263635426]
[74,0.12421092526617551]
[75,0.12106106866070887]
[76,0.68475583863770162]
[77,0.3577309741654357]
[78,0.31403120506579674]
[79,0.50992467977362466]
[80,0.16792113067475689]
[81,0.29637303629747636]
[82,0.23280444610347431]
[83,0.14139183352919696]
[84,0.66901361563570527]
[85,0.37707691993723969]
[86,0.1204031091163512]
[87,0.13162447550748194]
[88,0.17812030294462597]
[89,0.21555470832006587]
[90,0.6341633639046268]
[91,8.090420463124752E-2]
[92,0.23693734082848775]
[93,0.59852599191366251]
[94,0.20193469192904731]
[95,0.31649903299754001]
[96,7.775556133574596E-2]
[97,0.31440427498046225]
[98,0.21310042132528847]
[99,0.26469808638520226]
[100,0.37389369618743157]

{"sheet":"Binomial","index":2,"n_rows":103,"n_cols":16,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,0,0,8],[4,12,4,15],[14,12,14,14],[9,12,9,14],[10,12,10,14],[11,12,11,14],[12,12,12,14]]}
["UNIVARIATE BINOMIAL"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate #1","Uniform\nRandom\nVariate #2","Uniform\nRandom\nVariate #3","Uniform\nRandom\nVariate #4","Uniform\nRandom\nVariate #5","Uniform\nRandom\nVariate #6","Uniform\nRandom\nVariate #7","Binomial\nRandom \nVariate","Macro\nGenerated\nVariate, uniforms\nsubmitted","Macro\nGenerated\nVariate w/o\nUniforms\nsubmitted"]
[1,0.26868953420160424,0.44405580182317539,0.94465851721428806,0.49888612422971823,9.63488697880579E-2,9.3226344771026315E-2,0.11924615436169383,{"$f":"SUM(IF($B4:$H4<=$N$7,1,0))","v":6},{"$f":"Binomial($N$7,$N$8,$B4:$H4)","v":6},{"$f":"Binomial($N$7,$N$8)","v":4}]
[{"$f":"A4+1","v":2},0.79377423808874648,0.65718795300261768,8.3902096450906072E-2,0.59983503317384124,0.62426304440459734,0.91802688414454214,7.8087686772897458E-3,{"$f":"SUM(IF($B5:$H5<=$N$7,1,0))","v":6},6,7,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.22897348669921869,0.16854099652803767,0.7880284345439279,0.3099187159890805,0.85061759994125308,0.54577234848232525,{"$f":"SUM(IF($B6:$H6<=$N$7,1,0))","v":5},5,6,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.59746096109928493,0.92699625340972147,3.3603836690073163E-2,0.92758929924540767,0.96118627038557669,0.14065506242060088,{"$f":"SUM(IF($B7:$H7<=$N$7,1,0))","v":4},4,6,null,"prob = ",0.8,"Location","Any real number between 0 and 1, inclusive"]
[5,0.86717342695468203,0.12564729724809154,0.7808885858361172,0.67530632241603794,0.82805754970063883,0.87520177772951457,0.77070063697100721,{"$f":"SUM(IF($B8:$H8<=$N$7,1,0))","v":4},4,6,null,"k = ",7,"Shape","Any Finite Positive Integer"]
[6,0.27994300504477809,0.57228225911488473,0.55048393023289444,0.36090719085120559,0.14655897310343047,0.92739325317684185,0.15667105230573231,{"$f":"SUM(IF($B9:$H9<=$N$7,1,0))","v":6},6,7]
[7,0.93667220783619842,0.29739908159505091,0.74320952910312843,0.17084449145162306,3.7645333056332553E-2,5.1473729609779917E-2,0.55401585235608841,{"$f":"SUM(IF($B10:$H10<=$N$7,1,0))","v":6},6,5,null,"Distribution Type:",null,null,"Discrete"]
[8,0.43191155671140469,0.33552329929780045,0.23504453274061154,0.1289192128482497,0.99573050623093051,0.83358509352086874,0.27806884965063705,{"$f":"SUM(IF($B11:$H11<=$N$7,1,0))","v":5},5,7,null,"Distrbution Name:",null,null,"Binomial"]
[9,0.96203701528155405,0.79162900118788981,0.82409639266813339,0.88072724597550311,0.1036601397265301,0.26307517222225496,0.97908841635751276,{"$f":"SUM(IF($B12:$H12<=$N$7,1,0))","v":3},3,7,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,0.24822859655358209,9.4476181769571177E-2,0.43698633361489625,0.52802532605770924,0.23307076973984708,0.61743007445709308,{"$f":"SUM(IF($B13:$H13<=$N$7,1,0))","v":7},7,5,null,"Simulation Method:",null,null,"Convolution Method"]
[11,0.20171971836271319,0.14050226564731538,0.82450719990321852,0.42148541765256109,3.0325489419976703E-3,0.33326318867756177,0.80116780518975594,{"$f":"SUM(IF($B14:$H14<=$N$7,1,0))","v":5},5,4]
[12,0.58041618261550787,0.24325661202272519,0.2353386720939582,0.25639836713009945,0.81401486349769503,9.0828959308358992E-2,0.90758681691420595,{"$f":"SUM(IF($B15:$H15<=$N$7,1,0))","v":5},5,7,null,"Macro Format:",null,null,"=Binomial(prob, k, [unif])"]
[13,0.34366851316718994,0.66165916832683569,0.41783635199453883,0.22118218038386972,0.20130163587259031,0.34950246160939791,0.64123518709550864,{"$f":"SUM(IF($B16:$H16<=$N$7,1,0))","v":7},7,4]
[14,0.9651686825697714,0.56279612960791148,0.20895868808346618,0.46364262035621306,0.16972679136835811,0.14139170557370395,0.42552336256093326,{"$f":"SUM(IF($B17:$H17<=$N$7,1,0))","v":6},6,6]
[15,0.38704808829902526,0.97513917603786493,0.61849323117375588,0.10286499850614572,0.48366925251296766,0.9016041161399484,0.72679878758129601,{"$f":"SUM(IF($B18:$H18<=$N$7,1,0))","v":5},5,5,null,null,null,"Notes:","1. Uniform variables input to the macro can"]
[16,0.86385756571325945,0.43110523880919793,0.41341397746668018,0.1414194199651041,0.59472517243126566,0.76342508157800615,0.16572524205532524,{"$f":"SUM(IF($B19:$H19<=$N$7,1,0))","v":6},6,7,null,null,null,null,"be in a 1xk row vector or a kx1 column vector"]
[17,0.17476282037902591,8.3728507126800911E-2,0.45125352252218764,0.53115031103021348,0.37398147849794616,0.66961267637596589,0.67493411525208225,{"$f":"SUM(IF($B20:$H20<=$N$7,1,0))","v":7},7,5,null,null,null,null,"but the vector dimension (k) must match the"]
[18,0.38117659587117037,6.6163538436367908E-2,0.55095601736724475,0.24121868241910183,0.48619923140627641,0.55178239785731031,0.86008080692805722,{"$f":"SUM(IF($B21:$H21<=$N$7,1,0))","v":6},6,6,null,null,null,null,"k value provided or the macro will return an"]
[19,0.87794506028866293,5.8800603133947305E-2,0.76916565784570079,0.63154489097232969,0.28914261401619501,2.3419862767994681E-2,0.55094621250377018,{"$f":"SUM(IF($B22:$H22<=$N$7,1,0))","v":6},6,5,null,null,null,null,"error code."]
[20,0.18238019015349183,0.91427131754721946,0.2074303217864526,0.34259128604568745,0.52824300608824704,0.57238047928552127,0.70237562982859036,{"$f":"SUM(IF($B23:$H23<=$N$7,1,0))","v":6},6,6,null,null,null,null,"2. If a k-dimensional vector of uniform random"]
[21,0.39753335201985007,0.99208452571603889,0.98968210720256233,0.20615792323879945,0.30161026595052942,0.50035765055805559,1.0524162000349779E-2,{"$f":"SUM(IF($B24:$H24<=$N$7,1,0))","v":5},5,7,null,null,null,null,"variables is not provided to the macro, the"]
[22,0.74199757940000399,0.33932002996360344,0.29329530229659517,0.74672409361448933,0.57613284838298062,0.12278104423902592,0.67462563324256697,{"$f":"SUM(IF($B25:$H25<=$N$7,1,0))","v":7},7,7,null,null,null,null,"macro will generate all needed uniform"]
[23,0.57082894586967958,0.51026222064659499,0.64378712951547401,0.82493185552957493,0.91463687911771674,0.5076080193625998,0.66360191230678578,{"$f":"SUM(IF($B26:$H26<=$N$7,1,0))","v":5},5,6,null,null,null,null,"variables internally."]
[24,0.90195869363590486,0.68823388521184869,0.26034861785763719,0.43932967596023664,0.85435089758864236,0.74690899636827601,0.17395545948528424,{"$f":"SUM(IF($B27:$H27<=$N$7,1,0))","v":5},5,7]
[25,0.43843055863807978,0.3802352804098853,0.48875636874668416,0.98737245508274019,0.75550845086423768,0.35509000042603223,0.59480100668656222,{"$f":"SUM(IF($B28:$H28<=$N$7,1,0))","v":6},6,4]
[26,0.3929492390413114,0.81007583244623871,0.90611446184834976,0.73028965436657967,0.52300617319269782,0.87176304416969497,0.63173178226649018,{"$f":"SUM(IF($B29:$H29<=$N$7,1,0))","v":4},4,6]
[27,0.2515715048326993,7.1945023913193018E-2,0.50583283519150479,0.15100842200827502,3.6233927895830131E-2,0.38049179171909764,0.85016699205469193,{"$f":"SUM(IF($B30:$H30<=$N$7,1,0))","v":6},6,5]
[28,0.30550021398012439,6.0405119249104633E-2,0.34033602191558809,0.42209073630234029,0.31133184998632724,0.23369818567419975,0.72962648456275914,{"$f":"SUM(IF($B31:$H31<=$N$7,1,0))","v":7},7,5]
[29,7.9387447484473794E-2,0.36390303471752294,0.90607542650280681,0.75632244023626993,0.58036510544181064,0.69475809712404324,0.64068443059669566,{"$f":"SUM(IF($B32:$H32<=$N$7,1,0))","v":6},6,5]
[30,0.82057811417206794,2.3405931264653845E-2,0.7012680027746645,0.14225638890191872,0.75917254336870554,0.93463302896457301,0.18541556001810533,{"$f":"SUM(IF($B33:$H33<=$N$7,1,0))","v":5},5,7]
[31,5.0767455327721533E-3,0.72094892071410632,0.14077946580881839,0.82032331518940493,0.10776961308859778,0.12907395402798028,0.17053330229606589,{"$f":"SUM(IF($B34:$H34<=$N$7,1,0))","v":6},6,5]
[32,2.9980457362279278E-2,0.50045935317620716,0.32217442373509508,0.47869096147227719,0.55807866226191816,0.14831379773373055,0.1611329949618141,{"$f":"SUM(IF($B35:$H35<=$N$7,1,0))","v":7},7,5]
[33,0.89698739215075429,0.5185423769601476,0.41695106754313338,0.99239279451181472,5.968611419889347E-2,3.7519897421968373E-2,0.95365164737945263,{"$f":"SUM(IF($B36:$H36<=$N$7,1,0))","v":4},4,7]
[34,4.8518018441997213E-2,0.73465611364814176,0.45990089231225773,0.5773846898612669,0.13439929113262827,0.43375313990839715,0.2312891310468026,{"$f":"SUM(IF($B37:$H37<=$N$7,1,0))","v":7},7,4]
[35,0.37123916516677757,0.92262882703722793,0.60087959654199052,0.90528832704027873,0.47403175390697228,0.74613708590864314,0.51401655416016057,{"$f":"SUM(IF($B38:$H38<=$N$7,1,0))","v":5},5,5]
[36,0.18273885825049341,0.70297388611730971,0.41743434261957091,5.3776221000129243E-2,0.92463657425874057,4.4938495817940738E-2,0.74884577543770892,{"$f":"SUM(IF($B39:$H39<=$N$7,1,0))","v":6},6,5]
[37,0.12050005291704391,0.48699160733047131,0.79854695145178001,0.39489054994311357,4.3082671271250206E-2,5.1489985169852481E-3,0.66580405215093585,{"$f":"SUM(IF($B40:$H40<=$N$7,1,0))","v":7},7,6]
[38,0.64945693361731327,0.11771898978083439,3.1453777220467383E-2,2.3782779554623046E-2,0.80366524333729239,0.67667373800564989,0.98267258301130289,{"$f":"SUM(IF($B41:$H41<=$N$7,1,0))","v":5},5,5]
[39,0.84523354850406707,0.93147610649873314,0.7227030982250009,0.85963805879282773,0.43289966488460607,0.33526595300625361,0.68756227448055884,{"$f":"SUM(IF($B42:$H42<=$N$7,1,0))","v":4},4,5]
[40,0.96559113278394504,0.52180085869870974,0.36085133601913555,0.12440347074229197,0.89358801039548452,0.30700203175416052,0.65238038775693818,{"$f":"SUM(IF($B43:$H43<=$N$7,1,0))","v":5},5,5]
[41,0.66499232931154673,0.72501602030632817,0.38693248732470809,2.2260548661534929E-2,1.6525030432561372E-2,0.89518862995787418,0.88185734416296357,{"$f":"SUM(IF($B44:$H44<=$N$7,1,0))","v":5},5,7]
[42,0.48716817186481609,0.50203712162708591,0.61023482778033322,0.13104379579847802,0.94876941793097813,7.7893617773898138E-2,0.40175400334604028,{"$f":"SUM(IF($B45:$H45<=$N$7,1,0))","v":6},6,5]
[43,0.77210315614728597,0.45847626516131068,0.58003721433938082,0.44415130341552289,0.84265241818595837,0.76447272294425284,0.46249900968999003,{"$f":"SUM(IF($B46:$H46<=$N$7,1,0))","v":6},6,4]
[44,0.82636627627465631,0.2765273183663941,5.9388649347640765E-2,0.41267253660556658,0.94500924785849738,0.1629516516408539,0.35068718722389947,{"$f":"SUM(IF($B47:$H47<=$N$7,1,0))","v":5},5,6]
[45,0.30996283637913491,0.15196584628760113,0.92957314107007982,0.79261822755734368,0.90906594417631015,0.86652546747056636,6.9907098986668914E-2,{"$f":"SUM(IF($B48:$H48<=$N$7,1,0))","v":4},4,5]
[46,0.1840653161997976,0.40443685419245889,0.87408911659487432,0.25180653470572434,9.4276343175194621E-2,0.15668580202679661,0.1368271528970133,{"$f":"SUM(IF($B49:$H49<=$N$7,1,0))","v":6},6,7]
[47,0.58275788798882977,0.51568403043388444,0.44301428650688701,0.2451710697180467,0.39833740174041821,1.3944395329431925E-2,0.55781898761101589,{"$f":"SUM(IF($B50:$H50<=$N$7,1,0))","v":7},7,7]
[48,0.3211056530871087,0.88707475191810981,9.2598313034766844E-2,0.2891176650001267,0.50001696445442201,0.57007562577295368,0.88420600791876236,{"$f":"SUM(IF($B51:$H51<=$N$7,1,0))","v":5},5,2]
[49,0.94059973373021577,0.12199706419429013,0.57705540086425366,0.81808384594513595,4.5318035527652345E-2,0.94711126032404858,0.89140581044253508,{"$f":"SUM(IF($B52:$H52<=$N$7,1,0))","v":3},3,7]
[50,0.14907620621989892,0.5485823647611463,0.26796530810244401,0.21952720594787811,0.36154336839763968,0.31777841576637189,0.22763980918811466,{"$f":"SUM(IF($B53:$H53<=$N$7,1,0))","v":7},7,7]
[51,0.38302044178353878,0.54107979941368844,0.18711104130384804,0.36722038571383531,0.59813420561627439,0.9892828019299893,0.24495161099784046,{"$f":"SUM(IF($B54:$H54<=$N$7,1,0))","v":6},6,7]
[52,8.4815952479745493E-2,1.6353855701170983E-2,0.43364037164232572,0.23540635657850706,0.12507276441986082,0.3447163615124974,0.38457562033908521,{"$f":"SUM(IF($B55:$H55<=$N$7,1,0))","v":7},7,7]
[53,0.84221407414122895,0.4652930510870229,0.23495666686238392,7.1608469861346613E-2,0.84496171990889513,0.62492740094331245,0.92529320470534515,{"$f":"SUM(IF($B56:$H56<=$N$7,1,0))","v":4},4,5]
[54,0.40498559499715014,0.64175961031266415,0.17319708286410218,0.99569633649613354,7.3232864520601515E-3,1.2808531333711293E-2,0.39454366109127237,{"$f":"SUM(IF($B57:$H57<=$N$7,1,0))","v":6},6,6]
[55,0.31192254229901473,0.384294644489242,0.49906889542757915,0.58155200720445932,0.22075959401793743,0.67644331763222698,0.46032556339866315,{"$f":"SUM(IF($B58:$H58<=$N$7,1,0))","v":7},7,6]
[56,7.3945219604894419E-2,0.26715954448559143,0.53594573165479953,0.14378757291087185,0.78509729565243125,0.58076291586251172,0.73713309747665212,{"$f":"SUM(IF($B59:$H59<=$N$7,1,0))","v":7},7,4]
[57,0.41540561914582874,0.43564406875484152,0.76465240175288818,0.73597608744136589,0.44092761059884067,0.89141421781484664,9.5760459546443855E-2,{"$f":"SUM(IF($B60:$H60<=$N$7,1,0))","v":6},6,6]
[58,0.94334481547755944,0.64841364201228391,0.10106244218475435,0.37465241097256619,0.15885608636138859,0.28879635201970133,0.50521758873022016,{"$f":"SUM(IF($B61:$H61<=$N$7,1,0))","v":6},6,7]
[59,0.6294690698059815,0.31342593702642774,0.27999663957185783,0.797712258076687,0.97554420231398031,0.1778556759072395,0.9554329436906237,{"$f":"SUM(IF($B62:$H62<=$N$7,1,0))","v":5},5,5]
[60,0.21751765244325438,8.4241915546240942E-2,7.6231579349971379E-2,0.77883884135572168,4.2973587007961389E-2,0.46526317958107355,0.39204334912332972,{"$f":"SUM(IF($B63:$H63<=$N$7,1,0))","v":7},7,7]
[61,0.81132182231923589,0.68530048572932756,0.91843321793348964,0.87078609678800201,0.45717511120216625,0.76702017936304512,0.12070228102247393,{"$f":"SUM(IF($B64:$H64<=$N$7,1,0))","v":4},4,5]
[62,0.47641953418452843,0.49373831416690117,0.61116889863213786,0.13677772832920221,0.983538823626248,0.6915807454954539,0.96054304312971439,{"$f":"SUM(IF($B65:$H65<=$N$7,1,0))","v":5},5,4]
[63,0.92308615531225435,0.82856125921562329,0.67135354273510084,0.38706028641485202,0.94162374400265936,0.87575791579838369,0.47862942255948415,{"$f":"SUM(IF($B66:$H66<=$N$7,1,0))","v":3},3,7]
[64,0.62241658364570296,0.99521523300006831,0.15108467654332614,0.13182799022577973,0.20076209511189935,7.6786451973095415E-3,0.91073778351494639,{"$f":"SUM(IF($B67:$H67<=$N$7,1,0))","v":5},5,5]
[65,0.56290274788396399,0.57439239559870603,0.94001077530971422,0.79083059029753733,0.12868770780541583,0.49658633995084855,0.97282140880468793,{"$f":"SUM(IF($B68:$H68<=$N$7,1,0))","v":5},5,5]
[66,0.27617460253729631,0.90514549193163008,0.93238631014475204,0.72004724911869522,1.5207213473711012E-2,0.14124940681356268,0.97409958752198067,{"$f":"SUM(IF($B69:$H69<=$N$7,1,0))","v":4},{"$f":"Binomial($N$7,$N$8,$B69:$H69)","v":4},{"$f":"Binomial($N$7,$N$8)","v":2}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.42663573398542542,0.40268599968699748,0.46648308886850365,7.8097896811085921E-2,0.15469216615354309,0.10406671101240361,{"$f":"SUM(IF($B70:$H70<=$N$7,1,0))","v":6},6,5]
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[69,0.14106716857892998,0.41316596081555601,0.22786742823371819,0.67549286065820424,0.60628011623117506,0.7188258255753831,0.50860538327200566,{"$f":"SUM(IF($B72:$H72<=$N$7,1,0))","v":7},7,7]
[70,0.78799892820694739,0.10465423467224733,0.74837210120785669,0.79841454852660287,7.8566064599190577E-2,0.1515141803650254,0.80966139436599005,{"$f":"SUM(IF($B73:$H73<=$N$7,1,0))","v":6},6,7]
[71,0.62019869479720879,3.7197902037881203E-2,0.19416544327049856,0.12837160179383356,0.76430208946843625,0.4974618589726667,0.72600342230786075,{"$f":"SUM(IF($B74:$H74<=$N$7,1,0))","v":7},7,5]
[72,0.32070616340267466,0.34771751832010722,0.45035525860180958,0.64637311454866697,9.6923054175458656E-2,0.59979783204462722,0.87301022364969127,{"$f":"SUM(IF($B75:$H75<=$N$7,1,0))","v":6},6,5]
[73,0.71916827005391148,0.62919972857465234,0.11435596958412531,0.43942490070084406,0.9878691149045844,0.18127906494341761,6.3812019019040989E-2,{"$f":"SUM(IF($B76:$H76<=$N$7,1,0))","v":6},6,6]
[74,0.70290736382840724,0.33028691321614589,0.60341658426690092,0.98828558083875662,0.48942774820349144,3.5778795498131899E-2,1.3143018336182033E-2,{"$f":"SUM(IF($B77:$H77<=$N$7,1,0))","v":6},6,7]
[75,0.154172834186179,0.82934810072780096,0.97519129510717062,0.66863378854350475,0.57432083636357789,0.19329622125990009,0.64505361838847464,{"$f":"SUM(IF($B78:$H78<=$N$7,1,0))","v":5},5,6]
[76,0.27977295388613965,0.2479116645837256,0.90015875266033063,0.82798540785461017,0.75042584489901865,0.46445682008699596,0.78554631005836639,{"$f":"SUM(IF($B79:$H79<=$N$7,1,0))","v":5},5,6]
[77,0.42321062277449939,0.11691194355116818,0.18268005882632721,0.57863070299224251,0.65154362177907565,0.81331363482318131,0.34602150169604473,{"$f":"SUM(IF($B80:$H80<=$N$7,1,0))","v":6},6,5]
[78,0.98136142771892321,0.2126052668686973,0.49378432861767929,0.12917870966829981,0.17037939374521316,0.17639705247165427,0.61437131575961945,{"$f":"SUM(IF($B81:$H81<=$N$7,1,0))","v":6},6,4]
[79,0.20085756040090119,0.54482783306965632,0.15206980415878835,0.80649843587074299,0.46794337762397409,9.9669387719940383E-2,8.7422034934123372E-2,{"$f":"SUM(IF($B82:$H82<=$N$7,1,0))","v":6},6,5]
[80,0.16133779816984994,4.8198744566575136E-2,0.83830783611343196,0.18046025675183097,0.71784600312470304,0.72332414312747417,0.96761793291909071,{"$f":"SUM(IF($B83:$H83<=$N$7,1,0))","v":5},5,6]
[81,0.25863578352871763,0.42254787054736553,0.77893307474131113,0.14905719793036742,0.48267683924500737,0.36737654554779875,0.12522263003024947,{"$f":"SUM(IF($B84:$H84<=$N$7,1,0))","v":7},7,6]
[82,0.8347220398143228,0.39308391964321521,0.34844397558988538,0.68209905343015476,3.1969902411721485E-4,0.14905460173087837,4.836536615533038E-2,{"$f":"SUM(IF($B85:$H85<=$N$7,1,0))","v":6},6,6]
[83,0.51591167107959424,0.85182300536064515,0.29184570629979889,0.19791537152532712,8.343290608135856E-2,0.62569509198140727,0.18028680782988771,{"$f":"SUM(IF($B86:$H86<=$N$7,1,0))","v":6},6,6]
[84,0.24633192212221666,0.11812905311926203,0.8600294725604537,0.50617864033560112,0.9207569090563027,0.26636195462233647,0.7092825074676069,{"$f":"SUM(IF($B87:$H87<=$N$7,1,0))","v":5},5,6]
[85,0.59063871388364364,0.42056439810769575,0.80770427139800016,0.83277849811506122,0.17082366589778664,0.95643767012414227,0.49649529007552617,{"$f":"SUM(IF($B88:$H88<=$N$7,1,0))","v":4},4,5]
[86,0.65393134749071002,1.4831636671858162E-2,0.31721254355102813,0.25331650531851324,0.35754387192920722,8.8694904205437131E-2,0.5125265437487655,{"$f":"SUM(IF($B89:$H89<=$N$7,1,0))","v":7},7,5]
[87,0.56445460206933995,0.36716035465117058,0.14728906509629813,2.7228034984578153E-2,0.89765836586751635,0.41335975025087734,0.58564927042993487,{"$f":"SUM(IF($B90:$H90<=$N$7,1,0))","v":6},6,7]
[88,0.10565266639072934,0.2451461442845756,0.75699264474447314,0.18836523515263148,0.38905069115978863,0.91493203869986917,0.42026023075945995,{"$f":"SUM(IF($B91:$H91<=$N$7,1,0))","v":6},6,7]
[89,0.59226465879030998,0.20324185152060736,0.5569816922545987,0.82250809269997516,0.4961883902071127,0.35918682100226806,0.8565024038320761,{"$f":"SUM(IF($B92:$H92<=$N$7,1,0))","v":5},5,6]
[90,0.72089126375496948,0.6153593343442274,0.34490514828723084,0.64566155333166775,0.58820323178895351,0.28168345267729633,0.71170462173921156,{"$f":"SUM(IF($B93:$H93<=$N$7,1,0))","v":7},7,6]
[91,0.58803803186325454,0.23156698246912066,0.20833596652013231,5.9584644967523137E-2,0.25220618830623598,0.14212910625429498,0.85035345434684617,{"$f":"SUM(IF($B94:$H94<=$N$7,1,0))","v":6},6,6]
[92,0.76602838211191659,0.24775133853500109,0.74177770730494508,0.34224498107278167,0.71429842526070986,0.20540188219524902,0.61207450207107217,{"$f":"SUM(IF($B95:$H95<=$N$7,1,0))","v":7},7,6]
[93,0.48285856602942256,1.9371888135073734E-2,0.59734241484469186,8.8849935776666777E-2,0.76119032606566261,0.39076942525454483,0.59894725982057995,{"$f":"SUM(IF($B96:$H96<=$N$7,1,0))","v":7},7,6]
[94,0.62864718503333628,0.85525903591075469,0.72651082792566446,0.17568537894663494,0.65898770931263762,0.79790489759395022,0.72742497020319064,{"$f":"SUM(IF($B97:$H97<=$N$7,1,0))","v":6},6,5]
[95,0.33779794281158637,0.96600502897790752,0.72890849591978657,0.1676091166598157,0.10220556688681359,4.4334465319983418E-2,0.11393338647820017,{"$f":"SUM(IF($B98:$H98<=$N$7,1,0))","v":6},6,6]
[96,0.47576831339143399,0.12342088429061493,0.84500439278961514,0.37133314322368338,0.22985233234476043,0.53774209685275065,0.64227973468394028,{"$f":"SUM(IF($B99:$H99<=$N$7,1,0))","v":6},6,6]
[97,5.6312473117793416E-2,0.82615584090670624,0.39746820194220911,0.76770033709774821,0.78833912500599979,0.46660878586295595,0.86543242380584318,{"$f":"SUM(IF($B100:$H100<=$N$7,1,0))","v":5},5,5]
[98,0.80804733641082538,0.26781166835787318,0.15190694068306676,0.60802719908661262,0.42566726357463358,0.99783316657343102,0.75968364381620757,{"$f":"SUM(IF($B101:$H101<=$N$7,1,0))","v":5},5,5]
[99,0.49894266970018275,0.59543950981597049,0.48996129064447658,0.18064518783684902,0.67372558960368534,0.7458464568176949,0.79585881430679739,{"$f":"SUM(IF($B102:$H102<=$N$7,1,0))","v":7},7,4]
[100,0.32081795804802316,0.15219174065625574,0.12761995369866286,0.72357288320741242,0.46971588822023025,2.6892131528586716E-2,0.82342354055942402,{"$f":"SUM(IF($B103:$H103<=$N$7,1,0))","v":6},6,7]

{"sheet":"Cauchy","index":3,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,0,0,5],[4,6,4,9],[14,6,14,8],[9,6,9,8],[10,6,10,8],[11,6,11,8],[12,6,12,8]]}
["UNIVARIATE CAUCHY"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Cauchy\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7+$H$8*TAN(PI()*($B4-0.5))","v":-1.5558485691021944},{"$f":"cauchy($H$7,$H$8,$B4)","v":-1.5558485691021944},{"$f":"cauchy($H$7,$H$8)","v":-179.23608262835685}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7+$H$8*TAN(PI()*($B5-0.5))","v":7.2849903292034579},7.2849903292034579,{"$f":"cauchy($H$7,$H$8)","v":-4.2675211667092547},null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,8.3905276183428477,8.3905276183428477,-12.835847719610287,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,4.2848372614719334,4.2848372614719334,-1.2401129326489571,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,11.022778627156699,11.022778627156699,2.8313796920745689,null,"sigma = ",4,"Scale","Real number greater than zero"]
[6,0.27994300504477809,-1.3102943480098013,-1.3102943480098013,-3.1242145517572162]
[7,0.93667220783619842,21.839571906570857,21.839571906570857,-1.4967262653797482,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,1.1310820939877471,1.1310820939877471,6.6667496903867072,null,"Distrbution Name:",null,null,"Cauchy"]
[9,0.96203701528155405,35.379803690442557,35.379803690442557,3.9851352140800236,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,-6.3364539012180625,-6.3364539012180625,4.3756336839559484,null,"Simulation Method:",null,null,"Inverse Transform"]
[11,0.20171971836271319,-3.4434384195279772,-3.4434384195279772,-89.164132011177685]
[12,0.58041618261550787,3.0326019970639742,3.0326019970639742,33.824546554805181,null,"Macro Format:",null,null,"=Cauchy(mu, sigma, [unif])"]
[13,0.34366851316718994,-0.13936127496485584,-0.13936127496485584,-2.6930624808795951]
[14,0.9651686825697714,38.408429254302547,38.408429254302547,8.4379962528756955,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[15,0.38704808829902526,0.51786691042338329,0.51786691042338329,-10.253649088563252,null,null,null,null,"your own uniform random variable (unif). If"]
[16,0.86385756571325945,10.774910545590688,10.774910545590688,-4.8400351145300586,null,null,null,null,"not provided, the function will generate one"]
[17,0.17476282037902591,-4.5383373863190899,-4.5383373863190899,0.58453440471375684,null,null,null,null,"to be used in the formula."]
[18,0.38117659587117037,0.43336635436412418,0.43336635436412418,0.73100481203911194]
[19,0.87794506028866293,11.915346847991964,11.915346847991964,0.64040905725912989,null,null,null,null,"2. Column C shows the formula used in the"]
[20,0.18238019015349183,-4.2000255507015094,-4.2000255507015094,-371.66568652483073,null,null,null,null,"macro directly in the cell.  Column D generates"]
[21,0.39753335201985007,0.66596478911195556,0.66596478911195556,13.449970285369366,null,null,null,null,"the random variable with the macro, using the"]
[22,0.74199757940000399,5.8037692005555694,5.8037692005555694,-1.8801859371831968,null,null,null,null,"same uniform random variable (column A) as"]
[23,0.57082894586967958,2.9050496357522499,2.9050496357522499,-4.3771163011692886,null,null,null,null,"used in Column C, and therefore the output of"]
[24,0.90195869363590486,14.573470945885925,14.573470945885925,-910.36825693419757,null,null,null,null,"Columns C and D will match.  Column E runs"]
[25,0.43843055863807978,1.2164999210770344,1.2164999210770344,0.87723788633567379,null,null,null,null,"the macro using an internally generated "]
[26,0.3929492390413114,0.60163834984843256,0.60163834984843256,3.623973924182788,null,null,null,null,"uniform random input."]
[27,0.2515715048326993,-1.9606974939508954,-1.9606974939508954,109.8473978513105]
[28,0.30550021398012439,-0.80186669082260575,-0.80186669082260575,2.7974911382784056]
[29,7.9387447484473794E-2,-13.704373511442434,-13.704373511442434,1.399218781839791]
[30,0.82057811417206794,8.32836724211049,8.32836724211049,-4.327747368204454]
[31,5.0767455327721533E-3,-248.77711213805767,-248.77711213805767,3.425388967844111]
[32,2.9980457362279278E-2,-40.343327177705667,-40.343327177705667,1.9466453138098636]
[33,0.89698739215075429,13.925494674131473,13.925494674131473,207.60757525226765]
[34,4.8518018441997213E-2,-24.039064964339737,-24.039064964339737,8.3086088356797951]
[35,0.37123916516677757,0.2875022594983887,0.2875022594983887,-3.7663075989942021]
[36,0.18273885825049341,-4.1847165934415163,-4.1847165934415163,4.5041923959612049]
[37,0.12050005291704391,-8.056660068493132,-8.056660068493132,7.6905456942426937]
[38,0.64945693361731327,4.0295131645066,4.0295131645066,40.229088411333429]
[39,0.84523354850406707,9.5681076941793783,9.5681076941793783,-41.19253853017878]
[40,0.96559113278394504,38.858995283089065,38.858995283089065,10.277958531768709]
[41,0.66499232931154673,4.2814319668792802,4.2814319668792802,9.9613476548275237E-2]
[42,0.48716817186481609,1.8386630869772616,1.8386630869772616,-7.4431687753580587]
[43,0.77210315614728597,6.5979988653949633,6.5979988653949633,-0.91284125367623448]
[44,0.82636627627465631,8.5907402553592718,8.5907402553592718,0.60323666508095819]
[45,0.30996283637913491,-0.71907995075442699,-0.71907995075442699,5.603878060699258]
[46,0.1840653161997976,-4.1285598277236684,-4.1285598277236684,1657.7920554605143]
[47,0.58275788798882977,3.0640500732665092,3.0640500732665092,-3.7823892305822735]
[48,0.3211056530871087,-0.51903022233439078,-0.51903022233439078,5.9850506849779119]
[49,0.94059973373021577,23.185518262606902,23.185518262606902,2.7513099378610404]
[50,0.14907620621989892,-5.907088556417996,-5.907088556417996,-7.3059932543420025E-2]
[51,0.38302044178353878,0.46003087094994788,0.46003087094994788,0.55496294203510854]
[52,8.4815952479745493E-2,-12.654823960914504,-12.654823960914504,-2.2891873830295459]
[53,0.84221407414122895,9.3973926384918265,9.3973926384918265,8.0353638358781065E-3]
[54,0.40498559499715014,0.7692411679484692,0.7692411679484692,-9.9332374994356005]
[55,0.31192254229901473,-0.68322362717637697,-0.68322362717637697,1.2258077253467259]
[56,7.3945219604894419E-2,-14.90782523235756,-14.90782523235756,-4.1508879162517927]
[57,0.41540561914582874,0.91120055353056628,0.91120055353056628,10.957834647313755]
[58,0.94334481547755944,24.235667452057061,24.235667452057061,13.338376850933093]
[59,0.6294690698059815,3.7230390176733463,3.7230390176733463,-281.58246404248797]
[60,0.21751765244325438,-2.9126758713265408,-2.9126758713265408,-28.170804980563076]
[61,0.81132182231923589,7.938720064222025,7.938720064222025,2.9801760869641418]
[62,0.47641953418452843,1.7031358770848712,1.7031358770848712,5.0563766996350754]
[63,0.92308615531225435,18.230663877920069,18.230663877920069,-4.7104340255112129]
[64,0.62241658364570296,3.6189467158519379,3.6189467158519379,-7.7878089935324812]
[65,0.56290274788396399,2.8009121233102117,2.8009121233102117,-0.73699783476440572]
[66,0.27617460253729631,{"$f":"$H$7+$H$8*TAN(PI()*($B69-0.5))","v":-1.3908752411087586},{"$f":"cauchy($H$7,$H$8,$B69)","v":-1.3908752411087586},{"$f":"cauchy($H$7,$H$8)","v":-5.3990401981446556}]
[{"$f":"A69+1","v":67},0.98183097898545246,72.001375848262967,72.001375848262967,-0.25344740460187465]
[68,0.17855864253016906,-4.3665312047431541,-4.3665312047431541,-0.99907607980432234]
[69,0.14106716857892998,-6.4269826232006046,-6.4269826232006046,54.23162710342762]
[70,0.78799892820694739,7.0903665869806929,7.0903665869806929,2.7207522082617492]
[71,0.62019869479720879,3.5866010292291826,3.5866010292291826,25.332284876622428]
[72,0.32070616340267466,-0.52604686567025682,-0.52604686567025682,113.34292238292062]
[73,0.71916827005391148,5.2915208808167904,5.2915208808167904,-14.325991254689452]
[74,0.70290736382840724,4.9623651184243851,4.9623651184243851,9.8683556275343385]
[75,0.154172834186179,-5.6023919950918399,-5.6023919950918399,6.3749610068773714]
[76,0.27977295388613965,-1.3138964003741331,-1.3138964003741331,6.3997291946640074]
[77,0.42321062277449939,1.0158705529733378,1.0158705529733378,-0.69485122362033236]
[78,0.98136142771892321,70.233983927966619,70.233983927966619,4.1592224813204179]
[79,0.20085756040090119,-3.4744512733464363,-3.4744512733464363,-0.63635501629951419]
[80,0.16133779816984994,-5.2040868069757664,-5.2040868069757664,2.2122740283266613]
[81,0.25863578352871763,-1.78864141101129,-1.78864141101129,-3.9139282490955845]
[82,0.8347220398143228,8.9985391716617151,8.9985391716617151,3.1327477437753819]
[83,0.51591167107959424,2.2001186691002959,2.2001186691002959,0.57899306336834111]
[84,0.24633192212221666,-2.0932677615815907,-2.0932677615815907,34.545759637054509]
[85,0.59063871388364364,3.1708162989702573,3.1708162989702573,-4.774209990882964]
[86,0.65393134749071002,4.1007276141663258,4.1007276141663258,2.8654049932688239]
[87,0.56445460206933995,2.8212151049262424,2.8212151049262424,7.3556334727803581]
[88,0.10565266639072934,-9.6053405640371139,-9.6053405640371139,15.412698040118569]
[89,0.59226465879030998,3.1930324797767504,3.1930324797767504,-2.1070270671924058]
[90,0.72089126375496948,5.3279965930140012,5.3279965930140012,2.4202158568161463]
[91,0.58803803186325454,3.1354190506249378,3.1354190506249378,-18.731032312479691]
[92,0.76602838211191659,6.4245754368843375,6.4245754368843375,-9.247167956531106]
[93,0.48285856602942256,1.7843859225130894,1.7843859225130894,1.1636026493225975]
[94,0.62864718503333628,3.7108080639897603,3.7108080639897603,6.968034059441151]
[95,0.33779794281158637,-0.23519189947460895,-0.23519189947460895,-3.0330656651733099]
[96,0.47576831339143399,1.694906059403873,1.694906059403873,7.5592600626808615]
[97,5.6312473117793416E-2,-20.373883208282329,-20.373883208282329,1.6911647308575239]
[98,0.80804733641082538,7.8088482320427932,7.8088482320427932,-4.0757426343400045]
[99,0.49894266970018275,1.9867131467229593,1.9867131467229593,7.6685895700745945]
[100,0.32081795804802316,-0.5240821831443343,-0.5240821831443343,0.78445358590069003]

{"sheet":"Chi-Squared","index":4,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,0,0,4],[4,4,4,7],[13,4,13,6],[8,4,8,6],[9,4,9,6],[10,4,10,6],[11,4,11,6]]}
["UNIVARIATE CHI-SQUARED"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"Chisquared($F$7)","v":8.4589031460152668}]
[{"$f":"A4+1","v":2},7.5575358961343753,null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},27.498218979761432,null,null,"Name","Value","Type","Feasible Range"]
[4,20.431035752032479,null,null,"k = ",7,"Shape","Any Finite Positive Integer"]
[5,6.7532819339689496]
[6,5.6596615161541601,null,null,"Distribution Type:",null,null,"Continuous"]
[7,6.6806719178276195,null,null,"Distrbution Name:",null,null,"Chi-Squared"]
[8,3.5569532100964354,null,null,"Variate Number:",null,null,"Univariate"]
[9,9.2486713442395949,null,null,"Simulation Method:",null,null,"Convolution"]
[10,13.092059736247805]
[11,6.9805739890634522,null,null,"Macro Format:",null,null,"=Chisquared(k)"]
[12,4.1899284897429983]
[13,7.0951192928035143]
[14,4.8643704373748617]
[15,6.5327573076146983,null,null,null,null,"Notes:","1. The Chi-Squared distribution does not lend"]
[16,5.4482154622232635,null,null,null,null,null,"itself easily to a manual presentation so no"]
[17,3.9840695415075893,null,null,null,null,null,"manual example is provided here, only the"]
[18,3.6502875597286724,null,null,null,null,null,"output of the macro generated variates."]
[19,7.2754709872003183,null,null,null,null,null,"2.  The input parameter k is also commonly"]
[20,8.3750439024605701,null,null,null,null,null,"called the \"degrees of freedom\" of the"]
[21,13.555705243367846,null,null,null,null,null,"chi-squared distribution."]
[22,4.0339478742013988]
[23,4.9787906762143095]
[24,11.649592985281519]
[25,4.7365131378380125]
[26,9.6529014636785515]
[27,2.5798238044640889]
[28,2.4408080971642514]
[29,1.9254256056971735]
[30,7.7543743079757803]
[31,8.2346277046400989]
[32,14.084972755557759]
[33,2.1793638166765072]
[34,11.863981741441716]
[35,3.5087640717499182]
[36,0.90351644682432797]
[37,1.7992327617998416]
[38,17.241107532504579]
[39,1.8827274078881169]
[40,13.761815047345777]
[41,11.850144164901875]
[42,8.3699696456211097]
[43,6.3904104823040662]
[44,10.970997728333623]
[45,6.7675653933531423]
[46,7.0178128936904516]
[47,4.1607842312161933]
[48,5.9250244732862942]
[49,3.1683404024132567]
[50,5.3715847627206665]
[51,3.8271498112929594]
[52,11.466118543861841]
[53,12.282620994423171]
[54,15.056896661209368]
[55,8.0096764439987744]
[56,2.6243083653217596]
[57,15.092849128287444]
[58,3.207452917394642]
[59,7.5266095343152619]
[60,3.2850404087608283]
[61,5.1852870277210643]
[62,11.503723456362106]
[63,4.3872934169948996]
[64,1.9894389287296956]
[65,4.2669143559082476]
[66,{"$f":"Chisquared($F$7)","v":4.3403517097958364}]
[{"$f":"A69+1","v":67},1.9807678315191075]
[68,5.1792004467339563]
[69,6.4700597854529702]
[70,3.9632220731147658]
[71,5.2555078842889538]
[72,6.3570127551437157]
[73,11.199208580692677]
[74,16.647963700927349]
[75,10.102191906412186]
[76,3.9528738767889697]
[77,7.7427659594004892]
[78,5.5351263037227243]
[79,6.8428446695158165]
[80,9.4051877089426714]
[81,3.932972017004027]
[82,3.9847711418080616]
[83,17.420327931240717]
[84,9.9208868882685284]
[85,4.0588766738509925]
[86,1.9817354845701605]
[87,5.1312076125281338]
[88,6.86686391017916]
[89,7.7977556376730419]
[90,9.7098113307253424]
[91,15.474276603929985]
[92,5.436054767047322]
[93,5.8552093181370326]
[94,13.774178377720045]
[95,4.4541739497618194]
[96,3.8873510208043767]
[97,4.7799216861139309]
[98,9.8662898452657188]
[99,11.255916269644425]
[100,4.2371180247880389]

{"sheet":"Discrete Uniform","index":5,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,6,14,8],[0,0,0,5],[4,6,4,9],[9,6,9,8],[10,6,10,8],[11,6,11,8],[12,6,12,8]]}
["UNIVARIATE DISCRETE UNIFORM"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Discrete\nUniform\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7+FLOOR(($H$8-$H$7+1)*$B4,1)","v":2},{"$f":"discrete($H$7,$H$8,$B4)","v":2},{"$f":"discrete($H$7,$H$8)","v":1}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7+FLOOR(($H$8-$H$7+1)*$B5,1)","v":5},{"$f":"discrete($H$7,$H$8,$B5)","v":5},{"$f":"discrete($H$7,$H$8)","v":1},null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,5,5,4,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,4,4,2,null,"a = ",1,"Location","Any finite integer"]
[5,0.86717342695468203,6,6,2,null,"b = ",6,"Location","Any finite integer such that b >= a"]
[{"$f":"A8+1","v":6},0.27994300504477809,2,2,2]
[{"$f":"A9+1","v":7},0.93667220783619842,6,6,6,null,"Distribution Type:",null,null,"Discrete"]
[{"$f":"A10+1","v":8},0.43191155671140469,3,3,2,null,"Distrbution Name:",null,null,"Uniform"]
[{"$f":"A11+1","v":9},0.96203701528155405,6,6,2,null,"Variate Number:",null,null,"Univariate"]
[{"$f":"A12+1","v":10},0.14240354575933512,1,1,6,null,"Simulation Method:",null,null,"Inverse Transform"]
[{"$f":"A13+1","v":11},0.20171971836271319,2,2,4]
[{"$f":"A14+1","v":12},0.58041618261550787,4,4,2,null,"Macro Format:",null,null,"=discrete(a, b, [unif])"]
[{"$f":"A15+1","v":13},0.34366851316718994,3,3,3]
[{"$f":"A16+1","v":14},0.9651686825697714,6,6,2,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[{"$f":"A17+1","v":15},0.38704808829902526,3,3,1,null,null,null,null,"your own uniform random variable (unif). If"]
[{"$f":"A18+1","v":16},0.86385756571325945,6,6,1,null,null,null,null,"not provided, the function will generate one"]
[{"$f":"A19+1","v":17},0.17476282037902591,2,2,2,null,null,null,null,"to be used in the formula."]
[{"$f":"A20+1","v":18},0.38117659587117037,3,3,1,null,null,null,null,"2. Column C shows the formula used in the"]
[{"$f":"A21+1","v":19},0.87794506028866293,6,6,3,null,null,null,null,"macro directly in the cell.  Column D generates"]
[{"$f":"A22+1","v":20},0.18238019015349183,2,2,4,null,null,null,null,"the random variable with the macro, using the"]
[{"$f":"A23+1","v":21},0.39753335201985007,3,3,6,null,null,null,null,"same uniform random variable (column A) as"]
[{"$f":"A24+1","v":22},0.74199757940000399,5,5,5,null,null,null,null,"used in Column C, and therefore the output of"]
[{"$f":"A25+1","v":23},0.57082894586967958,4,4,1,null,null,null,null,"Columns C and D will match.  Column E runs"]
[{"$f":"A26+1","v":24},0.90195869363590486,6,6,6,null,null,null,null,"the macro using an internally generated "]
[{"$f":"A27+1","v":25},0.43843055863807978,3,3,3]
[{"$f":"A28+1","v":26},0.3929492390413114,3,3,3]
[{"$f":"A29+1","v":27},0.2515715048326993,2,2,5]
[{"$f":"A30+1","v":28},0.30550021398012439,2,2,5]
[{"$f":"A31+1","v":29},7.9387447484473794E-2,1,1,5]
[{"$f":"A32+1","v":30},0.82057811417206794,5,5,6]
[{"$f":"A33+1","v":31},5.0767455327721533E-3,1,1,5]
[{"$f":"A34+1","v":32},2.9980457362279278E-2,1,1,1]
[{"$f":"A35+1","v":33},0.89698739215075429,6,6,3]
[{"$f":"A36+1","v":34},4.8518018441997213E-2,1,1,1]
[{"$f":"A37+1","v":35},0.37123916516677757,3,3,3]
[{"$f":"A38+1","v":36},0.18273885825049341,2,2,6]
[{"$f":"A39+1","v":37},0.12050005291704391,1,1,6]
[{"$f":"A40+1","v":38},0.64945693361731327,4,4,3]
[{"$f":"A41+1","v":39},0.84523354850406707,6,6,3]
[{"$f":"A42+1","v":40},0.96559113278394504,6,6,6]
[{"$f":"A43+1","v":41},0.66499232931154673,4,4,5]
[{"$f":"A44+1","v":42},0.48716817186481609,3,3,3]
[{"$f":"A45+1","v":43},0.77210315614728597,5,5,1]
[{"$f":"A46+1","v":44},0.82636627627465631,5,5,3]
[{"$f":"A47+1","v":45},0.30996283637913491,2,2,4]
[{"$f":"A48+1","v":46},0.1840653161997976,2,2,5]
[{"$f":"A49+1","v":47},0.58275788798882977,4,4,5]
[{"$f":"A50+1","v":48},0.3211056530871087,2,2,2]
[{"$f":"A51+1","v":49},0.94059973373021577,6,6,6]
[{"$f":"A52+1","v":50},0.14907620621989892,1,1,1]
[{"$f":"A53+1","v":51},0.38302044178353878,3,3,6]
[{"$f":"A54+1","v":52},8.4815952479745493E-2,1,1,1]
[{"$f":"A55+1","v":53},0.84221407414122895,6,6,6]
[{"$f":"A56+1","v":54},0.40498559499715014,3,3,5]
[{"$f":"A57+1","v":55},0.31192254229901473,2,2,5]
[{"$f":"A58+1","v":56},7.3945219604894419E-2,1,1,1]
[{"$f":"A59+1","v":57},0.41540561914582874,3,3,2]
[{"$f":"A60+1","v":58},0.94334481547755944,6,6,6]
[{"$f":"A61+1","v":59},0.6294690698059815,4,4,4]
[{"$f":"A62+1","v":60},0.21751765244325438,2,2,3]
[{"$f":"A63+1","v":61},0.81132182231923589,5,5,2]
[{"$f":"A64+1","v":62},0.47641953418452843,3,3,1]
[{"$f":"A65+1","v":63},0.92308615531225435,6,6,6]
[{"$f":"A66+1","v":64},0.62241658364570296,4,4,1]
[{"$f":"A67+1","v":65},0.56290274788396399,4,4,4]
[{"$f":"A68+1","v":66},0.27617460253729631,{"$f":"$H$7+FLOOR(($H$8-$H$7+1)*$B69,1)","v":2},{"$f":"discrete($H$7,$H$8,$B69)","v":2},{"$f":"discrete($H$7,$H$8)","v":5}]
[{"$f":"A69+1","v":67},0.98183097898545246,6,6,3]
[68,0.17855864253016906,2,2,5]
[69,0.14106716857892998,1,1,3]
[70,0.78799892820694739,5,5,6]
[71,0.62019869479720879,4,4,4]
[72,0.32070616340267466,2,2,2]
[73,0.71916827005391148,5,5,1]
[74,0.70290736382840724,5,5,1]
[75,0.154172834186179,1,1,1]
[76,0.27977295388613965,2,2,5]
[77,0.42321062277449939,3,3,2]
[78,0.98136142771892321,6,6,2]
[79,0.20085756040090119,2,2,2]
[80,0.16133779816984994,1,1,5]
[81,0.25863578352871763,2,2,3]
[82,0.8347220398143228,6,6,5]
[83,0.51591167107959424,4,4,2]
[84,0.24633192212221666,2,2,2]
[85,0.59063871388364364,4,4,1]
[86,0.65393134749071002,4,4,2]
[87,0.56445460206933995,4,4,4]
[88,0.10565266639072934,1,1,5]
[89,0.59226465879030998,4,4,2]
[90,0.72089126375496948,5,5,5]
[91,0.58803803186325454,4,4,2]
[92,0.76602838211191659,5,5,5]
[93,0.48285856602942256,3,3,4]
[94,0.62864718503333628,4,4,6]
[95,0.33779794281158637,3,3,6]
[96,0.47576831339143399,3,3,2]
[97,5.6312473117793416E-2,1,1,5]
[98,0.80804733641082538,5,5,5]
[99,0.49894266970018275,3,3,4]
[100,0.32081795804802316,2,2,3]

{"sheet":"Erlang","index":6,"n_rows":103,"n_cols":16,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,0,0,5],[4,12,4,15],[14,12,14,14],[9,12,9,14],[10,12,10,14],[11,12,11,14],[12,12,12,14]]}
["UNIVARIATE ERLANG"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate #1","Uniform\nRandom\nVariate #2","Uniform\nRandom\nVariate #3","Uniform\nRandom\nVariate #4","Uniform\nRandom\nVariate #5","Uniform\nRandom\nVariate #6","Uniform\nRandom\nVariate #7","Erlang\nRandom \nVariate","Macro\nGenerated\nVariate, uniforms\nsubmitted","Macro\nGenerated\nVariate w/o\nUniforms\nsubmitted"]
[1,0.26868953420160424,0.44405580182317539,0.94465851721428806,0.49888612422971823,9.63488697880579E-2,9.3226344771026315E-2,0.11924615436169383,{"$f":"-(LN(PRODUCT($B4:$H4))/$N$7)","v":3.2391276302535825},{"$f":"Erlang($N$7,$N$8,$B4:$H4)","v":3.2391276302535825},{"$f":"Erlang($N$7,$N$8)","v":3.0780150621164628}]
[{"$f":"A4+1","v":2},0.79377423808874648,0.65718795300261768,8.3902096450906072E-2,0.59983503317384124,0.62426304440459734,0.91802688414454214,7.8087686772897458E-3,{"$f":"-(LN(PRODUCT($B5:$H5))/$N$7)","v":3.0163889153062606},3.0163889153062606,1.3792751970840025,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.22897348669921869,0.16854099652803767,0.7880284345439279,0.3099187159890805,0.85061759994125308,0.54577234848232525,1.8759254570560835,1.8759254570560835,1.2957728814165983,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.59746096109928493,0.92699625340972147,3.3603836690073163E-2,0.92758929924540767,0.96118627038557669,0.14065506242060088,2.1559525327295348,2.1559525327295348,2.165694636039194,null,"sigma =",3,"Scale","Real number greater than zero"]
[5,0.86717342695468203,0.12564729724809154,0.7808885858361172,0.67530632241603794,0.82805754970063883,0.87520177772951457,0.77070063697100721,1.1463777300039002,1.1463777300039002,5.059788553172857,null,"k = ",7,"Shape","Any Finite Positive Integer"]
[6,0.27994300504477809,0.57228225911488473,0.55048393023289444,0.36090719085120559,0.14655897310343047,0.92739325317684185,0.15667105230573231,2.4322320010566876,2.4322320010566871,1.6113959210015829]
[7,0.93667220783619842,0.29739908159505091,0.74320952910312843,0.17084449145162306,3.7645333056332553E-2,5.1473729609779917E-2,0.55401585235608841,3.3928910027363188,3.3928910027363188,1.6886099778774579,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,0.33552329929780045,0.23504453274061154,0.1289192128482497,0.99573050623093051,0.83358509352086874,0.27806884965063705,2.298110863067115,2.298110863067115,1.8694529938888229,null,"Distrbution Name:",null,null,"Erlang"]
[9,0.96203701528155405,0.79162900118788981,0.82409639266813339,0.88072724597550311,0.1036601397265301,0.26307517222225496,0.97908841635751276,1.4053087534774218,1.4053087534774218,3.6722568254281072,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,0.24822859655358209,9.4476181769571177E-2,0.43698633361489625,0.52802532605770924,0.23307076973984708,0.61743007445709308,3.0356566939251466,3.0356566939251466,1.4846498778457404,null,"Simulation Method:",null,null,"Convolution"]
[11,0.20171971836271319,0.14050226564731538,0.82450719990321852,0.42148541765256109,3.0325489419976703E-3,0.33326318867756177,0.80116780518975594,3.9130688759500507,3.9130688759500503,1.1977689501765612]
[12,0.58041618261550787,0.24325661202272519,0.2353386720939582,0.25639836713009945,0.81401486349769503,9.0828959308358992E-2,0.90758681691420595,2.4889735445011136,2.4889735445011136,1.7245602322696219,null,"Macro Format:",null,null,"=Erlang(sigma, k, [unif])"]
[13,0.34366851316718994,0.66165916832683569,0.41783635199453883,0.22118218038386972,0.20130163587259031,0.34950246160939791,0.64123518709550864,2.3203569638288868,2.3203569638288868,2.6784804797365283]
[14,0.9651686825697714,0.56279612960791148,0.20895868808346618,0.46364262035621306,0.16972679136835811,0.14139170557370395,0.42552336256093326,2.5095906766097706,2.5095906766097702,1.4154454781100514]
[15,0.38704808829902526,0.97513917603786493,0.61849323117375588,0.10286499850614572,0.48366925251296766,0.9016041161399484,0.72679878758129601,1.6260758712339378,1.6260758712339378,2.5065007729967053,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[16,0.86385756571325945,0.43110523880919793,0.41341397746668018,0.1414194199651041,0.59472517243126566,0.76342508157800615,0.16572524205532524,2.1380338762041879,2.1380338762041879,2.429561969391913,null,null,null,null,"your own uniform random variables (unif). If"]
[17,0.17476282037902591,8.3728507126800911E-2,0.45125352252218764,0.53115031103021348,0.37398147849794616,0.66961267637596589,0.67493411525208225,2.4768941775107329,2.4768941775107329,2.4105345429341698,null,null,null,null,"not provided, the function will generate all"]
[18,0.38117659587117037,6.6163538436367908E-2,0.55095601736724475,0.24121868241910183,0.48619923140627641,0.55178239785731031,0.86008080692805722,2.3882457189095967,2.3882457189095962,1.8932778369111709,null,null,null,null,"needed uniform RVs to be used in the formula."]
[19,0.87794506028866293,5.8800603133947305E-2,0.76916565784570079,0.63154489097232969,0.28914261401619501,2.3419862767994681E-2,0.55094621250377018,3.0923112351811644,3.0923112351811644,2.0565869678997535,null,null,null,null,"2. Uniform variables input to the macro can"]
[20,0.18238019015349183,0.91427131754721946,0.2074303217864526,0.34259128604568745,0.52824300608824704,0.57238047928552127,0.70237562982859036,1.9949679239866829,1.9949679239866829,1.6225912185795208,null,null,null,null,"be in a 1xk row vector or a kx1 column vector"]
[21,0.39753335201985007,0.99208452571603889,0.98968210720256233,0.20615792323879945,0.30161026595052942,0.50035765055805559,1.0524162000349779E-2,2.9883469840579249,2.9883469840579249,2.1078349275740846,null,null,null,null,"but the vector dimension (k) must match the"]
[22,0.74199757940000399,0.33932002996360344,0.29329530229659517,0.74672409361448933,0.57613284838298062,0.12278104423902592,0.67462563324256697,1.9800742370347812,1.9800742370347812,1.347870701826297,null,null,null,null,"k value provided or the macro will return an"]
[23,0.57082894586967958,0.51026222064659499,0.64378712951547401,0.82493185552957493,0.91463687911771674,0.5076080193625998,0.66360191230678578,1.0145615291921837,1.0145615291921835,1.0825592209149113,null,null,null,null,"error code."]
[24,0.90195869363590486,0.68823388521184869,0.26034861785763719,0.43932967596023664,0.85435089758864236,0.74690899636827601,0.17395545948528424,1.6144110636329219,1.6144110636329219,2.4992241875298635,null,null,null,null,"3. Column I shows the manual formula for"]
[25,0.43843055863807978,0.3802352804098853,0.48875636874668416,0.98737245508274019,0.75550845086423768,0.35509000042603223,0.59480100668656222,1.4517982231857109,1.4517982231857109,2.3911867805795506,null,null,null,null,"generating an Erlang variable, using the seven"]
[26,0.3929492390413114,0.81007583244623871,0.90611446184834976,0.73028965436657967,0.52300617319269782,0.87176304416969497,0.63173178226649018,0.93409864854289459,0.93409864854289459,2.5058781793413161,null,null,null,null,"uniform random variables provided.  Column J"]
[27,0.2515715048326993,7.1945023913193018E-2,0.50583283519150479,0.15100842200827502,3.6233927895830131E-2,0.38049179171909764,0.85016699205469193,3.6767407497804752,3.6767407497804752,2.563819481315603,null,null,null,null,"replicates those same calculuations via a macro,"]
[28,0.30550021398012439,6.0405119249104633E-2,0.34033602191558809,0.42209073630234029,0.31133184998632724,0.23369818567419975,0.72962648456275914,2.9562287600788473,2.9562287600788473,1.6945341248674481,null,null,null,null,"and the results in J should match those in I."]
[29,7.9387447484473794E-2,0.36390303471752294,0.90607542650280681,0.75632244023626993,0.58036510544181064,0.69475809712404324,0.64068443059669566,1.7585702494335917,1.7585702494335917,2.9472683318279289,null,null,null,null,"In Column K the macro is used without the"]
[30,0.82057811417206794,2.3405931264653845E-2,0.7012680027746645,0.14225638890191872,0.75917254336870554,0.93463302896457301,0.18541556001810533,2.7619282129688703,2.7619282129688703,3.4451818968722918,null,null,null,null,"provided seven uniform random variables, and"]
[31,5.0767455327721533E-3,0.72094892071410632,0.14077946580881839,0.82032331518940493,0.10776961308859778,0.12907395402798028,0.17053330229606589,4.6042810814603934,4.6042810814603925,1.8051218866149887,null,null,null,null,"instead internally generates seven uniform"]
[32,2.9980457362279278E-2,0.50045935317620716,0.32217442373509508,0.47869096147227719,0.55807866226191816,0.14831379773373055,0.1611329949618141,3.4620020771164164,3.4620020771164164,2.1059576963269269,null,null,null,null,"RVs for its own use."]
[33,0.89698739215075429,0.5185423769601476,0.41695106754313338,0.99239279451181472,5.968611419889347E-2,3.7519897421968373E-2,0.95365164737945263,2.5989554281412142,2.5989554281412142,2.5810627144880032]
[34,4.8518018441997213E-2,0.73465611364814176,0.45990089231225773,0.5773846898612669,0.13439929113262827,0.43375313990839715,0.2312891310468026,2.9888233750417128,2.9888233750417124,2.2352293857351491]
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["UNIVARIATE EXPONENTIAL"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Exponential\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
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[7,0.93667220783619842,5.5188619829358467,5.5188619829358467,3.470820077485171,null,"Distrbution Name:",null,null,"Exponential"]
[8,0.43191155671140469,1.1309563247347985,1.1309563247347985,2.5307251858567574,null,"Variate Number:",null,null,"Univariate"]
[9,0.96203701528155405,6.5422873606857257,6.5422873606857257,3.2796166037637531,null,"Simulation Method:",null,null,"Inverse Transform"]
[10,0.14240354575933512,0.30724324637659345,0.30724324637659345,1.9677994141415034]
[11,0.20171971836271319,0.45059102615455032,0.45059102615455032,0.48804751361169835,null,"Macro Format:",null,null,"=Exponential(sigma, [unif])"]
[12,0.58041618261550787,1.7369839399417795,1.7369839399417795,1.4629572545080884E-2]
[13,0.34366851316718994,0.84217860474581996,0.84217860474581996,1.6855446041303557,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[14,0.9651686825697714,6.7144767414729616,6.7144767414729616,2.5054000559425629,null,null,null,null,"your own uniform random variable (unif). If"]
[15,0.38704808829902526,0.97893758718590218,0.97893758718590218,1.3052836357766757,null,null,null,null,"not provided, the function will generate one"]
[16,0.86385756571325945,3.9881072607232917,3.9881072607232917,1.4634008029262429,null,null,null,null,"to be used within the macro."]
[17,0.17476282037902591,0.38416888703050217,0.38416888703050217,1.9617259001439575]
[18,0.38117659587117037,0.95987067840016993,0.95987067840016993,1.1744791924974256,null,null,null,null,"2. Column C shows the formula used in the"]
[19,0.87794506028866293,4.2065680202244327,4.2065680202244327,0.75562654287872311,null,null,null,null,"macro directly in the cell.  Column D generates"]
[20,0.18238019015349183,0.40271566112380153,0.40271566112380153,3.0114766353283913,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,1.0134459423981468,1.0134459423981468,1.1017812615080976E-2,null,null,null,null,"same uniform random variable (column A) as"]
[22,0.74199757940000399,2.7095726238680093,2.7095726238680093,2.5695405380782383,null,null,null,null,"used in Column C, and therefore the output of"]
[23,0.57082894586967958,1.6917994238966634,1.6917994238966634,0.82638217623273535,null,null,null,null,"Columns C and D will match.  Column E runs"]
[24,0.90195869363590486,4.6447327912076553,4.6447327912076553,2.8733495069890131,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,1.1540396825606996,1.1540396825606996,2.00230069243168,null,null,null,null,"uniform random input."]
[26,0.3929492390413114,0.99828573091499773,0.99828573091499773,0.30179753587981278]
[27,0.2515715048326993,0.5795592210488496,0.5795592210488496,2.5165148017380945]
[28,0.30550021398012439,0.7291268497890333,0.7291268497890333,0.94053242051283703]
[29,7.9387447484473794E-2,0.16543202509164984,0.16543202509164984,1.6190063047422958]
[30,0.82057811417206794,3.436030684433228,3.436030684433228,0.13856274807134997]
[31,5.0767455327721533E-3,1.0179351974046232E-2,1.0179351974046232E-2,0.2635454593389327]
[32,2.9980457362279278E-2,6.0878121276921993E-2,6.0878121276921993E-2,0.12399647482391976]
[33,0.89698739215075429,4.5458077838803703,4.5458077838803703,1.0503706516544131]
[34,4.8518018441997213E-2,9.9469058611899183E-2,9.9469058611899183E-2,1.9875388366666134]
[35,0.37123916516677757,0.92800865075508399,0.92800865075508399,0.10780046586610217]
[36,0.18273885825049341,0.40359320050036751,0.40359320050036751,3.9449253863525151E-2]
[37,0.12050005291704391,0.25680354994343269,0.25680354994343269,1.6668403094045794]
[38,0.64945693361731327,2.0965434175565383,2.0965434175565383,1.6467582642153284]
[39,0.84523354850406707,3.7316761258330615,3.7316761258330615,2.722378669102973]
[40,0.96559113278394504,6.738881959821299,6.738881959821299,5.573100499159799]
[41,0.66499232931154673,2.1872036996834874,2.1872036996834874,0.44292506901849416]
[42,0.48716817186481609,1.3356146159109448,1.3356146159109448,0.21475097183998865]
[43,0.77210315614728597,2.9577243833033897,2.9577243833033897,1.2898054701929236]
[44,0.82636627627465631,3.5016144690628805,3.5016144690628805,2.3224734223203933]
[45,0.30996283637913491,0.74201964504230522,0.74201964504230522,4.1924230964127709]
[46,0.1840653161997976,0.40684194316849609,0.40684194316849609,3.3995634573790094]
[47,0.58275788798882977,1.7481772426509821,1.7481772426509821,1.8300595130252244]
[48,0.3211056530871087,0.77457952908495287,0.77457952908495287,0.26247393201061658]
[49,0.94059973373021577,5.6469131399345693,5.6469131399345693,1.0265513031787568]
[50,0.14907620621989892,0.32286540688614856,0.32286540688614856,1.0375413436973435]
[51,0.38302044178353878,0.96583877311030208,0.96583877311030208,3.141168087483293]
[52,8.4815952479745493E-2,0.17726017820529136,0.17726017820529136,0.89832280346682003]
[53,0.84221407414122895,3.693032128579266,3.693032128579266,1.2132850037241087]
[54,0.40498559499715014,1.0383393272814869,1.0383393272814869,9.2464548916229766E-2]
[55,0.31192254229901473,0.74770772703634047,0.74770772703634047,1.3515037437048214]
[56,7.3945219604894419E-2,0.1536437759833244,0.1536437759833244,1.6618656455702741]
[57,0.41540561914582874,1.07367407660189,1.07367407660189,4.5669304981189676]
[58,0.94334481547755944,5.7415435544119999,5.7415435544119999,1.2148444467370256]
[59,0.6294690698059815,1.9856367108508119,1.9856367108508119,4.2257836225580832]
[60,0.21751765244325438,0.49056783171040108,0.49056783171040108,1.3388721559600278]
[61,0.81132182231923589,3.3354249577320689,3.3354249577320689,0.17269160762651073]
[62,0.47641953418452843,1.2941291061988305,1.2941291061988305,0.44762430292334376]
[63,0.92308615531225435,5.1301387674474137,5.1301387674474137,0.24326511684705651]
[64,0.62241658364570296,1.9479275284569562,1.9479275284569562,9.6987118513433241]
[65,0.56290274788396399,1.6551991275160658,1.6551991275160658,0.41878663057343524]
[66,0.27617460253729631,{"$f":"-$H$7*LN(1-$B69)","v":0.64641015881323105},{"$f":"Exponential($H$7,$B69)","v":0.64641015881323105},{"$f":"Exponential($H$7)","v":1.3917078221854784}]
[{"$f":"A69+1","v":67},0.98183097898545246,8.0160745544939473,8.0160745544939473,1.8486465007679784]
[68,0.17855864253016906,0.39338945750350163,0.39338945750350163,4.8121878221010297]
[69,0.14106716857892998,0.30412910795421316,0.30412910795421316,0.80396123758225158]
[70,0.78799892820694739,3.102327897390595,3.102327897390595,1.6263892207584658]
[71,0.62019869479720879,1.936214088113914,1.936214088113914,5.600597126192441]
[72,0.32070616340267466,0.77340299198706064,0.77340299198706064,2.6492572893662132]
[73,0.71916827005391148,2.5399992296616225,2.5399992296616225,4.5309737468129576]
[74,0.70290736382840724,2.4274225650208732,2.4274225650208732,1.0665167763404091]
[75,0.154172834186179,0.33488047195094539,0.33488047195094539,3.6482255904551919]
[76,0.27977295388613965,0.65637754971402629,0.65637754971402629,7.6918697391287809]
[77,0.42321062277449939,1.1005562198380487,1.1005562198380487,0.76909889456139702]
[78,0.98136142771892321,7.9650441340420457,7.9650441340420457,3.0185971436531944]
[79,0.20085756040090119,0.44843215353037985,0.44843215353037985,5.4447291879115074E-2]
[80,0.16133779816984994,0.35189454715204449,0.35189454715204449,3.6009349700418634]
[81,0.25863578352871763,0.59852650847675615,0.59852650847675615,0.65872822236856599]
[82,0.8347220398143228,3.6002532305094945,3.6002532305094945,0.46722423129152041]
[83,0.51591167107959424,1.4509757822935281,1.4509757822935281,1.1283944255017448]
[84,0.24633192212221666,0.56560644582691877,0.56560644582691877,1.0990558853767611]
[85,0.59063871388364364,1.7863143454336852,1.7863143454336852,0.20048710124876207]
[86,0.65393134749071002,2.1222362118993705,2.1222362118993705,5.1598251168262612]
[87,0.56445460206933995,1.6623124897667099,1.6623124897667099,0.45702681128309663]
[88,0.10565266639072934,0.2233221258401763,0.2233221258401763,1.3923603364243675]
[89,0.59226465879030998,1.7942739771266445,1.7942739771266445,0.71394673862980274]
[90,0.72089126375496948,2.5523076748854208,2.5523076748854208,1.8429237555215212]
[91,0.58803803186325454,1.7736484884823565,1.7736484884823565,1.6635733409656666]
[92,0.76602838211191659,2.9051109241147195,2.9051109241147195,1.5404900808087727]
[93,0.48285856602942256,1.318877750424033,1.318877750424033,4.5360665745818247]
[94,0.62864718503333628,1.9812053690712448,1.9812053690712448,3.8922026388459967]
[95,0.33779794281158637,0.82436909455399499,0.82436909455399499,1.7481732534631895]
[96,0.47576831339143399,1.2916430847285252,1.2916430847285252,6.136020339430889]
[97,5.6312473117793416E-2,0.11592035458221038,0.11592035458221038,0.84637922606440186]
[98,0.80804733641082538,3.3010129623153164,3.3010129623153164,2.8591416299904719]
[99,0.49894266970018275,1.3820695054158436,1.3820695054158436,1.5379887378351373]
[100,0.32081795804802316,0.77373216866915306,0.77373216866915306,2.0809542081413204]

{"sheet":"F Distribution","index":8,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,4,14,6],[0,0,0,4],[4,4,4,7],[9,4,9,6],[10,4,10,6],[11,4,11,6],[12,4,12,6]]}
["UNIVARIATE F-DISTRIBUTION"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"Fdistribution($F$7,$F$8)","v":2.0320337019313978E-2}]
[{"$f":"A4+1","v":2},0.30430685482591102,null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.18110912241230886,null,null,"Name","Value","Type","Feasible Range"]
[4,0.41432229580046764,null,null,"k1 = ",2,"Shape","Any Finite Positive Integer"]
[5,0.41760416908778192,null,null,"k2 = ",7,"Shape","Any Finite Positive Integer"]
[6,1.5814127485767822]
[7,0.65629325537495087,null,null,"Distribution Type:",null,null,"Continuous"]
[8,0.11369540688478026,null,null,"Distrbution Name:",null,null,"F-Distribution"]
[9,0.61436106939475243,null,null,"Variate Number:",null,null,"Univariate"]
[10,1.0391790781173811,null,null,"Simulation Method:",null,null,"Convolution"]
[11,0.79551945753751896]
[12,12.165210433891799,null,null,"Macro Format:",null,null,"=Fdistribution(k1, k2)"]
[13,2.094518892426863]
[14,0.21140330383270642]
[15,4.208164317310259,null,null,null,null,"Notes:","1. The F distribution does not lend itself"]
[16,9.0331439728501088,null,null,null,null,null,"easily to a manual presentation so no manual"]
[17,0.17540841469092988,null,null,null,null,null,"example is provided here, only the output"]
[18,2.62536619344961E-2,null,null,null,null,null,"of the macro generated variates."]
[19,0.58881910824212857,null,null,null,null,null,"2.  The input parameters k1 and k2 are also"]
[20,0.60886012941252288,null,null,null,null,null,"commonly called the \"degrees of freedom\" of"]
[21,0.12058510334117645,null,null,null,null,null,"the F distribution."]
[22,1.7291253862795533]
[23,0.86845026235968703]
[24,1.1579840386005702]
[25,2.0998350049983525]
[26,1.0800246016703716]
[27,0.96332322732280928]
[28,0.10723127666797094]
[29,7.7122615721753656]
[30,1.6443656896882761]
[31,0.21667647933983944]
[32,0.33091311296840475]
[33,1.1594844683263967]
[34,7.2885856845211733E-2]
[35,0.32110550558066259]
[36,0.78787209517084589]
[37,0.31435742325981686]
[38,1.3847577743371817]
[39,2.9173151206563346]
[40,2.3882678204230494]
[41,3.1293831259483103]
[42,0.87106142664706876]
[43,3.4704810429968452E-2]
[44,2.1762468871682885]
[45,3.3465679685339991]
[46,5.4942435322260881]
[47,0.5228796590261463]
[48,5.6763889788108726]
[49,0.92302898479898188]
[50,1.8485077547468414]
[51,0.99594683995023103]
[52,9.4877638291396842]
[53,0.11198921762870991]
[54,1.7313210593503241]
[55,1.1171735045921076]
[56,7.1797988365135357]
[57,6.1859523993686789]
[58,1.2516202224319135]
[59,0.44412903942659326]
[60,0.41750874378223435]
[61,2.4679515115335176]
[62,4.5499100367116014]
[63,3.7342241022913716]
[64,4.368481993670672]
[65,4.4101278324336501]
[66,{"$f":"Fdistribution($F$7,$F$8)","v":0.26402485043630414}]
[{"$f":"A69+1","v":67},0.16631060394257324]
[68,1.2206958891933697]
[69,0.11506122729415325]
[70,1.494784700336431]
[71,2.7235584424375365]
[72,0.45216819504392208]
[73,6.3335825713013385]
[74,0.94901181374626531]
[75,1.2087907212318905]
[76,6.1610507564769854]
[77,0.18724090396925402]
[78,2.4275951273836363]
[79,1.1681839018073923]
[80,4.183688499096315E-2]
[81,0.23056913029838938]
[82,0.46120005262909691]
[83,0.86842508529269891]
[84,0.75465770037498781]
[85,2.4184038447005078]
[86,0.52921225499963886]
[87,0.6370670104614391]
[88,0.26994428978857865]
[89,0.49320075649969486]
[90,0.2185591501595075]
[91,0.32071116334209204]
[92,7.0393887436727782]
[93,3.2262554627592448]
[94,0.79124961114865577]
[95,0.85958353562365375]
[96,2.2365556219189897]
[97,2.990432535458865]
[98,0.33466344660302699]
[99,0.78664076807136396]
[100,3.9703342209338457]

{"sheet":"Frechet","index":9,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[15,6,15,8],[0,0,0,5],[4,6,4,9],[10,6,10,8],[11,6,11,8],[12,6,12,8],[13,6,13,8]]}
["UNIVARIATE FRÉCHET"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Fréchet\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7+$H$8*(-LN($B4))^(-1/$H$9)","v":3.7446144961551009},{"$f":"Frechet($H$7,$H$8,$H$9,$B4)","v":3.7446144961551009},{"$f":"Frechet($H$7,$H$8,$H$9)","v":3.5565969675459002}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7+$H$8*(-LN($B5))^(-1/$H$9)","v":6.1616465197564141},6.1616465197564141,6.3626738065453026,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,6.517092583442575,6.517092583442575,4.0470241395680784,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,5.1323790467712662,5.1323790467712662,6.5625180250917117,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,7.2978266035628305,7.2978266035628296,4.2900042540235521,null,"sigma = ",2,"Scale","Real number greater than zero"]
[6,0.27994300504477809,3.7725027809881433,3.7725027809881428,3.3461155360179839,null,"alpha =",2,"Shape","Real number greater than zero"]
[7,0.93667220783619842,9.8193104107279794,9.8193104107279794,3.7221410009491382]
[8,0.43191155671140469,4.1827838751931976,4.1827838751931976,3.5833750990064188,null,"Distribution Type:",null,null,"Continuous"]
[9,0.96203701528155405,12.166262480115378,12.166262480115378,5.1668404313785343,null,"Distrbution Name:",null,null,"Fréchet"]
[10,0.14240354575933512,3.4325639122655005,3.4325639122655005,5.9325269796780677,null,"Variate Number:",null,null,"Univariate"]
[11,0.20171971836271319,3.580706132496136,3.580706132496136,3.8384396203105231,null,"Simulation Method:",null,null,"Inverse Transform"]
[12,0.58041618261550787,4.7116061077210283,4.7116061077210283,4.2069684720376097]
[13,0.34366851316718994,3.9352120948124019,3.9352120948124014,4.9835879471665674,null,"Macro Format:",null,null,"=Frechet(mu, sigma, alpha, [unif])"]
[14,0.9651686825697714,12.622022629212116,12.622022629212116,3.2669406707606994]
[15,0.38704808829902526,4.0528143822631257,4.0528143822631257,3.5196179735714259,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[16,0.86385756571325945,7.2280233946563559,7.2280233946563559,2.9310918713776721,null,null,null,null,"your own uniform random variable (unif). If"]
[17,0.17476282037902591,3.5143150070036842,3.5143150070036846,5.6656018077385912,null,null,null,null,"not provided, the function will generate one"]
[18,0.38117659587117037,4.0364819591552337,4.0364819591552337,3.8470246347586268,null,null,null,null,"to be used within the macro."]
[19,0.87794506028866293,7.5433517793713198,7.5433517793713198,4.3207831910487391,null,null,null,null,"2. Column C shows the formula used in the"]
[20,0.18238019015349183,3.5331807898344709,3.5331807898344709,4.9198427252165455,null,null,null,null,"macro directly in the cell.  Column D generates"]
[21,0.39753335201985007,4.0823434116790214,4.0823434116790214,3.7176559980971251,null,null,null,null,"the random variable with the macro, using the"]
[22,0.74199757940000399,5.6612030889579907,5.6612030889579907,3.4949244714475705,null,null,null,null,"same uniform random variable (column A) as"]
[23,0.57082894586967958,4.6710253390319547,4.6710253390319538,7.2373519550434651,null,null,null,null,"used in Column C, and therefore the output of"]
[24,0.90195869363590486,8.226133675582421,8.226133675582421,3.6003719047331648,null,null,null,null,"Columns C and D will match.  Column E runs"]
[25,0.43843055863807978,4.2025231719186174,4.2025231719186174,4.5622348150669083,null,null,null,null,"the macro using an internally generated "]
[26,0.3929492390413114,4.0693748136446057,4.0693748136446057,3.1544782768478834,null,null,null,null,"uniform random input."]
[27,0.2515715048326993,3.7024957797915912,3.7024957797915912,5.0347287844758961]
[28,0.30550021398012439,3.8366372728792966,3.8366372728792966,3.807347246547502]
[29,7.9387447484473794E-2,3.2565414677641198,3.2565414677641202,6.4757196585820473]
[30,0.82057811417206794,6.4975495371101335,6.4975495371101335,3.6176622905726727]
[31,5.0767455327721533E-3,2.8701341268340776,2.8701341268340776,4.4905246358306012]
[32,2.9980457362279278E-2,3.0679456210715075,3.0679456210715075,4.2776265495528243]
[33,0.89698739215075429,8.0658031378439397,8.0658031378439414,4.6488481181866117]
[34,4.8518018441997213E-2,3.1497633172262001,3.1497633172262001,4.2673669512566166]
[35,0.37123916516677757,4.0091536871526348,4.0091536871526348,7.0049417024905472]
[36,0.18273885825049341,3.5340666287913738,3.5340666287913738,3.4033981764186025]
[37,0.12050005291704391,3.374869190868214,3.374869190868214,6.0513842125651385]
[38,0.64945693361731327,5.0442466956245315,5.0442466956245315,8.4510360060133678]
[39,0.84523354850406707,6.8774351348758964,6.8774351348758964,3.5649752781388893]
[40,0.96559113278394504,12.688191293195693,12.688191293195693,3.8237233857784658]
[41,0.66499232931154673,5.1311990715116966,5.1311990715116966,5.000355555241347]
[42,0.48716817186481609,4.358421868822921,4.3584218688229219,5.4266766829577042]
[43,0.77210315614728597,5.9326434321872235,5.9326434321872235,5.9231736607488408]
[44,0.82636627627465631,6.5796796369477573,6.5796796369477581,5.1377188244672922]
[45,0.30996283637913491,3.8479720216576365,3.8479720216576365,4.0773857487625076]
[46,0.1840653161997976,3.5373409592157055,3.5373409592157059,4.0650716960568039]
[47,0.58275788798882977,4.7216969388662955,4.7216969388662955,4.5945943268160718]
[48,0.3211056530871087,3.876478891354187,3.8764788913541866,3.2000132574513378]
[49,0.94059973373021577,10.082038989257295,10.082038989257295,9.6780505891961059]
[50,0.14907620621989892,3.4496949954765252,3.4496949954765252,5.6018720668228834]
[51,0.38302044178353878,4.0415956590365596,4.0415956590365596,4.3239804245798155]
[52,8.4815952479745493E-2,3.2732729496762891,3.2732729496762891,3.7314571772365968]
[53,0.84221407414122895,6.8263434659978506,6.8263434659978506,3.7779392464305888]
[54,0.40498559499715014,4.1036277650748705,4.1036277650748705,7.5726725356024769]
[55,0.31192254229901473,3.8529639131809961,3.8529639131809965,3.6790461680094086]
[56,7.3945219604894419E-2,3.2392918387695833,3.2392918387695833,3.9173802662571928]
[57,0.41540561914582874,4.1338267349919295,4.1338267349919295,4.1658062210838498]
[58,0.94334481547755944,10.281491482633459,10.281491482633459,4.1904873351872691]
[59,0.6294690698059815,4.9396556644960334,4.9396556644960334,5.7076002501845728]
[60,0.21751765244325438,3.6193003499689622,3.6193003499689622,3.9066250134150362]
[61,0.81132182231923589,6.3738397159398259,6.3738397159398259,6.5974932811324081]
[62,0.47641953418452843,4.3226682067867053,4.3226682067867053,7.5103743619970853]
[63,0.92308615531225435,9.0696228342819154,9.0696228342819136,4.5772300174324556]
[64,0.62241658364570296,4.9045182190313206,4.9045182190313206,4.9662309068090238]
[65,0.56290274788396399,4.6383286460651165,4.6383286460651165,7.9638492070552109]
[66,0.27617460253729631,{"$f":"$H$7+$H$8*(-LN($B69))^(-1/$H$9)","v":3.7631433895650721},{"$f":"Frechet($H$7,$H$8,$H$9,$B69)","v":3.7631433895650721},{"$f":"Frechet($H$7,$H$8,$H$9)","v":4.2237515869350002}]
[{"$f":"A69+1","v":67},0.98183097898545246,16.7698626529628,16.7698626529628,4.0398213977321014]
[68,0.17855864253016906,3.5237290555108229,3.5237290555108229,6.1496154676110972]
[69,0.14106716857892998,3.4291114105485923,3.4291114105485923,6.8367687952734455]
[70,0.78799892820694739,6.0973753381956701,6.097375338195671,3.6232675819218185]
[71,0.62019869479720879,4.8936459039458429,4.8936459039458429,3.2192644320138304]
[72,0.32070616340267466,3.8754515560562179,3.8754515560562184,4.534473196055389]
[73,0.71916827005391148,5.4833484816595242,5.4833484816595242,3.2350201451292175]
[74,0.70290736382840724,5.3684635433781169,5.368463543378116,3.7580343378166106]
[75,0.154172834186179,3.4626696083554638,3.4626696083554642,5.5651210841266874]
[76,0.27977295388613965,3.7720799592731895,3.77207995927319,3.3891847127962063]
[77,0.42321062277449939,4.1567993001936863,4.1567993001936863,6.1544101913988358]
[78,0.98136142771892321,16.580893012646019,16.580893012646019,11.981748168949073]
[79,0.20085756040090119,3.5785957495926342,3.5785957495926342,3.5276015210874236]
[80,0.16133779816984994,3.4807686957291111,3.4807686957291111,9.012134824738899]
[81,0.25863578352871763,3.7198395826800521,3.7198395826800521,3.8848378800512968]
[82,0.8347220398143228,6.7054721187802047,6.7054721187802055,3.7240274926492569]
[83,0.51591167107959424,4.4584430244043576,4.4584430244043576,3.7650566386823421]
[84,0.24633192212221666,3.6896596987432555,3.6896596987432555,5.4328749693740734]
[85,0.59063871388364364,4.7561945712777778,4.7561945712777778,5.3507464796689792]
[86,0.65393134749071002,5.0687521666852149,5.0687521666852149,4.5122921277608334]
[87,0.56445460206933995,4.644671434228548,4.644671434228548,6.9798137928034691]
[88,0.10565266639072934,3.3340455191588445,3.3340455191588441,4.256164477471339]
[89,0.59226465879030998,4.7634177955708248,4.7634177955708248,3.4213877817827298]
[90,0.72089126375496948,5.4960602652533161,5.4960602652533161,5.3850634910928763]
[91,0.58803803186325454,4.7447171713068457,4.7447171713068457,9.4687098086650607]
[92,0.76602838211191659,5.8739321576658874,5.8739321576658874,3.0820294253230722]
[93,0.48285856602942256,4.3439854566278981,4.3439854566278981,6.8183110111854264]
[94,0.62864718503333628,4.935515654229734,4.935515654229734,4.8955859056959241]
[95,0.33779794281158637,3.9197895380948804,3.91978953809488,7.6474202444670052]
[96,0.47576831339143399,4.3205287336237559,4.3205287336237559,4.2766886885484237]
[97,5.6312473117793416E-2,3.1791585385619259,3.1791585385619259,3.9095915882367853]
[98,0.80804733641082538,6.3321449399247092,6.3321449399247092,4.2871912161940884]
[99,0.49894266970018275,4.3985849219080428,4.3985849219080428,3.6169453783310201]
[100,0.32081795804802316,3.8757390081092744,3.8757390081092744,4.3603495292886976]

{"sheet":"Gamma","index":10,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,4,14,6],[0,0,0,4],[4,4,4,7],[9,4,9,6],[10,4,10,6],[11,4,11,6],[12,4,12,6]]}
["UNIVARIATE GAMMA"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"Gammarv($F$7,$F$8)","v":0.1786565800619557}]
[{"$f":"A4+1","v":2},{"$f":"Gammarv($F$7,$F$8)","v":9.3861972814391542E-2},null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.37800809243656641,null,null,"Name","Value","Type","Feasible Range"]
[4,1.5623340934080757E-2,null,null,"alpha = ",1,"Shape","Any Finite Positive Real Number"]
[{"$f":"A7+1","v":5},6.8231015339160275E-3,null,null,"beta = ",5,"Scale","Any Finite Positive Real Number"]
[6,0.46497248661584445]
[7,1.2684537806694087E-2,null,null,"Distribution Type:",null,null,"Continuous"]
[8,0.68669955259351401,null,null,"Distrbution Name:",null,null,"Gamma"]
[9,0.22822616874312493,null,null,"Variate Number:",null,null,"Univariate"]
[10,2.0394910455368769E-2,null,null,"Simulation Method:",null,null,"Convolution"]
[11,3.9133923152924258E-2]
[12,3.8659684576975509E-2,null,null,"Macro Format:",null,null,"=Gammarv(alpha, beta)"]
[13,0.17125805358119295]
[14,0.2154421716330733]
[15,0.30548628308119052]
[16,0.12179313799036121,null,null,null,null,"Notes:","1. The Gamma distribution does not lend"]
[17,0.43858154134631749,null,null,null,null,null,"itself easily to a manual presentation so no"]
[18,0.42345111788211859,null,null,null,null,null,"manual example is provided here, only the"]
[19,0.24803938445124735,null,null,null,null,null,"output of the macro generated variates."]
[20,0.56299304835812281]
[21,0.1837078506412505]
[22,9.4083475860620644E-2]
[23,2.785447059318296E-2]
[24,0.32609305878635564]
[25,5.8831885853024388E-2]
[26,0.11183175565682364]
[27,0.19843870739673569]
[28,5.1377890289470471E-2]
[29,6.1684105395454367E-2]
[30,1.607631023022368E-4]
[31,9.6035837769294669E-2]
[32,6.9487615635777907E-3]
[33,0.46536983127752451]
[34,3.9103823051327743E-2]
[35,4.8033722397503795E-2]
[36,0.14119378192346291]
[{"$f":"A39+1","v":37},0.1065508035204964]
[38,0.1786279201871829]
[39,8.4675340319674497E-2]
[40,8.3194680548643221E-2]
[41,9.9188935407923465E-2]
[42,0.15630575194015867]
[43,0.13106383657689624]
[44,1.3021315491658936]
[45,0.27392051942541268]
[46,0.37558794045592842]
[47,7.4360021699016912E-2]
[48,0.30478860245158818]
[49,0.17806963720563598]
[50,0.51124204215071289]
[51,1.2997500888120874E-2]
[52,0.1972331866427097]
[53,0.27308502780397181]
[54,1.3436333635059674E-3]
[55,0.11028010749112742]
[56,0.18660586080853853]
[57,0.40026603305447817]
[58,6.9915701813290196E-2]
[59,0.30801754972509066]
[60,0.1596917630655223]
[61,0.38799704952275149]
[62,0.29712152147162185]
[63,4.6437954466857702E-2]
[64,0.19206168522062489]
[65,0.20826810765813816]
[66,{"$f":"Gammarv($F$7,$F$8)","v":3.1086819686488139E-2}]
[{"$f":"A69+1","v":67},0.30666901930480528]
[68,0.19021035294586419]
[69,3.7443258775250246E-2]
[70,0.16853719053417496]
[71,0.13342359285815905]
[72,0.22172332602242517]
[73,0.35680988988082729]
[74,1.4773535600358225]
[75,0.23356711468580021]
[76,0.40708916149609237]
[77,0.26435343390171162]
[78,4.5896602852758359E-2]
[79,0.1759466862462728]
[80,0.34446083736940064]
[81,0.31235925692139344]
[82,3.8651867154164271E-2]
[83,0.17900931241728318]
[84,5.821775967392976E-2]
[85,0.12172543049342197]
[86,1.672255115991475E-2]
[87,0.55537539433719185]
[88,0.16820682715078586]
[89,0.11117672774992034]
[90,0.69941507906332034]
[91,6.2625660382462228E-2]
[92,5.0768928674142344E-2]
[93,7.839546035148269E-2]
[94,0.13185757374032719]
[95,0.11788183563583943]
[96,0.21581026481924165]
[97,0.37701454611089946]
[98,0.18266279829811058]
[99,0.20265469209934239]
[100,0.19352886932722821]

{"sheet":"Geometric","index":11,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[13,6,13,8],[0,0,0,5],[4,6,4,9],[8,6,8,8],[9,6,9,8],[10,6,10,8],[11,6,11,8]]}
["UNIVARIATE GEOMETRIC"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Geometric\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"FLOOR(LN($B4)/LN(1-$H$7),1)","v":5},{"$f":"geometric($H$7,$B4)","v":5},{"$f":"geometric($H$7)","v":8}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"FLOOR(LN($B5)/LN(1-$H$7),1)","v":1},1,0,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0,0,1,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,1,1,0,null,"prob = ",0.2,"Location","Any real number between 0 and 1, inclusive"]
[5,0.86717342695468203,0,0,0]
[6,0.27994300504477809,5,5,0,null,"Distribution Type:",null,null,"Discrete"]
[7,0.93667220783619842,0,0,0,null,"Distrbution Name:",null,null,"Geometric"]
[8,0.43191155671140469,3,3,8,null,"Variate Number:",null,null,"Univariate"]
[9,0.96203701528155405,0,0,1,null,"Simulation Method:",null,null,"Convolution"]
[10,0.14240354575933512,8,8,1]
[11,0.20171971836271319,7,7,2,null,"Macro Format:",null,null,"=Geometric(prob, [unif])"]
[12,0.58041618261550787,2,2,5]
[13,0.34366851316718994,4,4,1,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[14,0.9651686825697714,0,0,0,null,null,null,null,"your own uniform random variable (unif). If"]
[15,0.38704808829902526,4,4,2,null,null,null,null,"not provided, the function will generate one"]
[16,0.86385756571325945,0,0,8,null,null,null,null,"to be used in the formula."]
[17,0.17476282037902591,7,7,4,null,null,null,null,"2. Column C shows the formula used in the"]
[18,0.38117659587117037,4,4,6,null,null,null,null,"macro directly in the cell.  Column D generates"]
[19,0.87794506028866293,0,0,0,null,null,null,null,"the random variable with the macro, using the"]
[20,0.18238019015349183,7,7,4,null,null,null,null,"same uniform random variable (column A) as"]
[21,0.39753335201985007,4,4,3,null,null,null,null,"used in Column C, and therefore the output of"]
[22,0.74199757940000399,1,1,4,null,null,null,null,"Columns C and D will match.  Column E runs"]
[23,0.57082894586967958,2,2,3,null,null,null,null,"the macro using an internally generated "]
[24,0.90195869363590486,0,0,1,null,null,null,null,"uniform random input."]
[25,0.43843055863807978,3,3,13]
[26,0.3929492390413114,4,4,3]
[27,0.2515715048326993,6,6,2]
[28,0.30550021398012439,5,5,1]
[29,7.9387447484473794E-2,11,11,0]
[30,0.82057811417206794,0,0,0]
[31,5.0767455327721533E-3,23,23,0]
[32,2.9980457362279278E-2,15,15,19]
[33,0.89698739215075429,0,0,2]
[34,4.8518018441997213E-2,13,13,2]
[35,0.37123916516677757,4,4,7]
[36,0.18273885825049341,7,7,1]
[37,0.12050005291704391,9,9,11]
[38,0.64945693361731327,1,1,3]
[39,0.84523354850406707,0,0,0]
[40,0.96559113278394504,0,0,6]
[41,0.66499232931154673,1,1,1]
[42,0.48716817186481609,3,3,1]
[43,0.77210315614728597,1,1,9]
[44,0.82636627627465631,0,0,3]
[45,0.30996283637913491,5,5,13]
[46,0.1840653161997976,7,7,1]
[47,0.58275788798882977,2,2,2]
[48,0.3211056530871087,5,5,18]
[49,0.94059973373021577,0,0,3]
[50,0.14907620621989892,8,8,5]
[51,0.38302044178353878,4,4,1]
[52,8.4815952479745493E-2,11,11,4]
[53,0.84221407414122895,0,0,2]
[54,0.40498559499715014,4,4,10]
[55,0.31192254229901473,5,5,0]
[56,7.3945219604894419E-2,11,11,0]
[57,0.41540561914582874,3,3,0]
[58,0.94334481547755944,0,0,2]
[59,0.6294690698059815,2,2,1]
[60,0.21751765244325438,6,6,1]
[61,0.81132182231923589,0,0,6]
[62,0.47641953418452843,3,3,3]
[63,0.92308615531225435,0,0,6]
[64,0.62241658364570296,2,2,3]
[65,0.56290274788396399,2,2,6]
[66,0.27617460253729631,{"$f":"FLOOR(LN($B69)/LN(1-$H$7),1)","v":5},{"$f":"geometric($H$7,$B69)","v":5},{"$f":"geometric($H$7)","v":1}]
[{"$f":"A69+1","v":67},0.98183097898545246,0,0,0]
[68,0.17855864253016906,7,7,1]
[69,0.14106716857892998,8,8,7]
[70,0.78799892820694739,1,1,2]
[71,0.62019869479720879,2,2,5]
[72,0.32070616340267466,5,5,5]
[73,0.71916827005391148,1,1,11]
[74,0.70290736382840724,1,1,0]
[75,0.154172834186179,8,8,8]
[76,0.27977295388613965,5,5,4]
[77,0.42321062277449939,3,3,0]
[78,0.98136142771892321,0,0,2]
[79,0.20085756040090119,7,7,1]
[80,0.16133779816984994,8,8,1]
[81,0.25863578352871763,6,6,3]
[82,0.8347220398143228,0,0,3]
[83,0.51591167107959424,2,2,7]
[84,0.24633192212221666,6,6,7]
[85,0.59063871388364364,2,2,2]
[86,0.65393134749071002,1,1,7]
[87,0.56445460206933995,2,2,1]
[88,0.10565266639072934,10,10,1]
[89,0.59226465879030998,2,2,2]
[90,0.72089126375496948,1,1,2]
[91,0.58803803186325454,2,2,9]
[92,0.76602838211191659,1,1,3]
[93,0.48285856602942256,3,3,15]
[94,0.62864718503333628,2,2,9]
[95,0.33779794281158637,4,4,3]
[96,0.47576831339143399,3,3,1]
[97,5.6312473117793416E-2,12,12,2]
[98,0.80804733641082538,0,0,7]
[99,0.49894266970018275,3,3,8]
[100,0.32081795804802316,5,5,9]

{"sheet":"GEV","index":12,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[15,6,15,8],[0,0,0,8],[10,6,10,8],[11,6,11,8],[12,6,12,8],[13,6,13,8],[4,6,4,9]]}
["UNIVARIATE GENERALIZED EXTREME VALUE (GEV)"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","GEV\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7-($H$8/$H$9)*(1-(-LN($B4))^(-$H$9))","v":1.3275119490992362},{"$f":"GEV($H$7,$H$8,$H$9,$B4)","v":1.3275119490992362},{"$f":"GEV($H$7,$H$8,$H$9)","v":0.98453375684388833}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7-($H$8/$H$9)*(1-(-LN($B5))^(-$H$9))","v":18.019202968743592},18.019202968743596,0.17907611494595743,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,23.041830887340559,23.041830887340563,0.54415098261664885,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,7.6835680023809951,7.6835680023809942,1.7419396010944437,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,37.173480744510314,37.173480744510314,1.6494593016865104,null,"sigma = ",3,"Scale","Real number greater than zero"]
[6,0.27994300504477809,1.3921972911816911,1.3921972911816911,2.1662499484993938,null,"alpha =",1.5,"Shape","Real number greater than zero"]
[7,0.93667220783619842,119.52131725967256,119.52131725967253,68.602601926355021]
[8,0.43191155671140469,2.5999932429312298,2.5999932429312298,1.8651364575209906,null,"Distribution Type:",null,null,"Continuous"]
[9,0.96203701528155405,262.67815910811782,262.67815910811777,2.8606288718361768,null,"Distrbution Name:",null,null,"Generalized Extreme Value (GEV)"]
[10,0.14240354575933512,0.73499101259280186,0.73499101259280186,4.8345224973303864,null,"Variate Number:",null,null,"Univariate"]
[11,0.20171971836271319,0.98740068282891524,0.98740068282891524,58.505414723549819,null,"Simulation Method:",null,null,"Inverse Transform"]
[12,0.58041618261550787,4.9844795558217134,4.9844795558217143,1.1617707369706105]
[13,0.34366851316718994,1.8118645070599428,1.8118645070599428,0.85898238634598956,null,"Macro Format:",null,null,"=GEV(mu, sigma, alpha, [unif])"]
[14,0.9651686825697714,299.61370535369758,299.61370535369741,11.584700833437882]
[15,0.38704808829902526,2.1626640148179082,2.1626640148179082,0.86102899864854088,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[16,0.86385756571325945,35.723382656925914,35.723382656925914,4.0079512304816189,null,null,null,null,"your own uniform random variable (unif). If"]
[17,0.17476282037902591,0.86813784202817512,0.86813784202817512,1.27269639109885,null,null,null,null,"not provided, the function will generate one"]
[18,0.38117659587117037,2.1114544162453792,2.1114544162453792,2.4621717391931113,null,null,null,null,"to be used within the macro."]
[19,0.87794506028866293,42.585066292264109,42.585066292264116,4.956919487211719,null,null,null,null,"2. Column C shows the formula used in the"]
[20,0.18238019015349183,0.90099030098199129,0.90099030098199129,0.71696840703118925,null,null,null,null,"macro directly in the cell.  Column D generates"]
[21,0.39753335201985007,2.2573404722954886,2.2573404722954886,1.3535558814948843,null,null,null,null,"the random variable with the macro, using the"]
[22,0.74199757940000399,12.269065047445839,12.269065047445837,10.91885280770553,null,null,null,null,"same uniform random variable (column A) as"]
[23,0.57082894586967958,4.7640250101067236,4.7640250101067236,0.35869576855337049,null,null,null,null,"used in Column C, and therefore the output of"]
[24,0.90195869363590486,60.338614135011198,60.338614135011206,5.5749166850046112,null,null,null,null,"Columns C and D will match.  Column E runs"]
[25,0.43843055863807978,2.671169622634737,2.6711696226347366,0.9857349532168227,null,null,null,null,"the macro using an internally generated "]
[26,0.3929492390413114,2.2154272109852493,2.2154272109852493,0.84164083913417942,null,null,null,null,"uniform random input."]
[27,0.2515715048326993,1.2336675484536548,1.2336675484536548,3.1523513772736944]
[28,0.30550021398012439,1.5488529587372253,1.5488529587372253,11.889539326143614]
[29,7.9387447484473794E-2,0.49598721889021569,0.49598721889021569,0.34330775141647063]
[30,0.82057811417206794,22.744053857274803,22.744053857274803,0.29106152974462041]
[31,5.0767455327721533E-3,0.16470190218961811,0.16470190218961833,234.0444416990878]
[32,2.9980457362279278E-2,0.30450009093537123,0.30450009093537145,24.680499248106536]
[33,0.89698739215075429,55.796241192829704,55.79624119282969,0.96501935865272359]
[34,4.8518018441997213E-2,0.37998403858658159,0.37998403858658159,5.7610591389838879]
[35,0.37123916516677757,2.0275869381874729,2.0275869381874729,5.0295612404357017]
[36,0.18273885825049341,0.90255292206274484,0.90255292206274484,1.1099974434138198]
[37,0.12050005291704391,0.64971687813410206,0.64971687813410206,1.5784173516654183]
[38,0.64945693361731327,7.0530918343455333,7.0530918343455333,7.4065686751364872]
[39,0.84523354850406707,29.007781530204312,29.007781530204308,17.944566836772164]
[40,0.96559113278394504,305.24788450740328,305.24788450740334,1.7845405957660505]
[41,0.66499232931154673,7.6748880133716195,7.6748880133716204,2.460288939220467]
[42,0.48716817186481609,3.2794762376460072,3.2794762376460072,0.27446530753941945]
[43,0.77210315614728597,15.205255510304401,15.205255510304402,8.7502596596907676]
[44,0.82636627627465631,24.012938304887573,24.012938304887577,1.1395554673856609]
[45,0.30996283637913491,1.5777063873732489,1.5777063873732489,8.6936044600051883]
[46,0.1840653161997976,0.90834452588185632,0.90834452588185632,2.2962597101001494]
[47,0.58275788798882977,5.040333849990021,5.0403338499900201,1.1920025792060456]
[48,0.3211056530871087,1.6518517157584156,1.6518517157584156,2.0523382917769104]
[49,0.94059973373021577,131.97839189761672,131.97839189761669,5.5070557603629835]
[50,0.14907620621989892,0.76167539715264088,0.76167539715264088,0.79947049081985555]
[51,0.38302044178353878,2.127400267576073,2.127400267576073,1.5896446592448243]
[52,8.4815952479745493E-2,0.51606516753489062,0.51606516753489062,2.0033416558090473]
[53,0.84221407414122895,28.105717984413442,28.105717984413449,1.0664319408097822]
[54,0.40498559499715014,2.3272695729912138,2.3272695729912138,2664.5660214613076]
[55,0.31192254229901473,1.5905264400399175,1.5905264400399177,5.4208869677191887]
[56,7.3945219604894419E-2,0.47583981476816462,0.47583981476816462,0.90602319465384529]
[57,0.41540561914582874,2.4289437931296121,2.4289437931296121,10.92642025187817]
[58,0.94334481547755944,141.99259206233475,141.99259206233478,2.514155484114649]
[59,0.6294690698059815,6.3508140376583313,6.3508140376583304,6.7260369257062624]
[60,0.21751765244325438,1.061505473513138,1.061505473513138,1.3494256723218727]
[61,0.81132182231923589,20.918406589205208,20.918406589205215,1.3969327539719005]
[62,0.47641953418452843,3.1325754095353049,3.1325754095353044,1.500183148436828]
[63,0.92308615531225435,88.334172061261825,88.334172061261839,1.4507665510682195]
[64,0.62241658364570296,6.1257930907086164,6.1257930907086164,18.512287956175015]
[65,0.56290274788396399,4.5912050285238495,4.5912050285238504,7.6981885650680644]
[66,0.27617460253729631,{"$f":"$H$7-($H$8/$H$9)*(1-(-LN($B69))^(-$H$9))","v":1.3702597731877586},{"$f":"GEV($H$7,$H$8,$H$9,$B69)","v":1.3702597731877584},{"$f":"GEV($H$7,$H$8,$H$9)","v":17.01829489755594}]
[{"$f":"A69+1","v":67},0.98183097898545246,805.50711146811318,805.50711146811364,0.94599225253540187]
[68,0.17855864253016906,0.8844295730277838,0.8844295730277838,0.33218617838446773]
[69,0.14106716857892998,0.72968978923428329,0.72968978923428307,4.0509671068493107]
[70,0.78799892820694739,17.197180754994179,17.197180754994172,1.8831013959642326]
[71,0.62019869479720879,6.0572592896197301,6.057259289619731,3.0029363833233726]
[72,0.32070616340267466,1.6491401318315391,1.6491401318315388,1.3955192074678799]
[73,0.71916827005391148,10.566490862782995,10.566490862782997,9.0913365201044183]
[74,0.70290736382840724,9.5551071776030199,9.5551071776030199,26.632329905009811]
[75,0.154172834186179,0.78230971148993245,0.78230971148993245,0.60713017975418726]
[76,0.27977295388613965,1.391201223625921,1.391201223625921,1.4705641024333826]
[77,0.42321062277449939,2.5082406990967558,2.5082406990967558,14.169583258509647]
[78,0.98136142771892321,774.98336178061356,774.98336178061368,13.414872400691696]
[79,0.20085756040090119,0.98345115799428173,0.98345115799428173,7.3779560866061624]
[80,0.16133779816984994,0.81171146934870553,0.81171146934870531,6.7437927857240956]
[81,0.25863578352871763,1.2717560992459622,1.2717560992459624,26.463134579551163]
[82,0.8347220398143228,26.046514921751349,26.046514921751349,4.3200651999507427]
[83,0.51591167107959424,3.7146718265196577,3.7146718265196581,1.4821360557904217]
[84,0.24633192212221666,1.2059734459583751,1.2059734459583753,1.3634141285924173]
[85,0.59063871388364364,5.2344327871129863,5.2344327871129872,3.0245068736990897]
[86,0.65393134749071002,7.2247938065529409,7.2247938065529409,1.1282570370527014]
[87,0.56445460206933995,4.6243977546343711,4.6243977546343711,0.46602719249281943]
[88,0.10565266639072934,0.5935426809922304,0.5935426809922304,0.82959408379438226]
[89,0.59226465879030998,5.2756947399823195,5.2756947399823195,0.25735693752616751]
[90,0.72089126375496948,10.682594415690598,10.6825944156906,3.8911509247356588]
[91,0.58803803186325454,5.169312729972793,5.169312729972793,59.750846887263201]
[92,0.76602838211191659,14.534364292369293,14.534364292369295,4.4419472031996108]
[93,0.48285856602942256,3.2196209667421591,3.2196209667421591,0.33187143551627529]
[94,0.62864718503333628,6.3240196502629242,6.3240196502629242,2.4123403050028682]
[95,0.33779794281158637,1.7688901787060611,1.7688901787060611,0.38446616319298754]
[96,0.47576831339143399,3.1239268783624166,3.1239268783624161,23.573438541123817]
[97,5.6312473117793416E-2,0.40987988830202493,0.40987988830202493,1.6371151803035067]
[98,0.80804733641082538,20.325860641574618,20.325860641574621,3.4175189416826002]
[99,0.49894266970018275,3.449890466337151,3.4498904663371515,4.82008290715003]
[100,0.32081795804802316,1.6498985433885356,1.6498985433885356,6.3227979319671652]

{"sheet":"Gompertz","index":13,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,6,14,8],[0,0,0,5],[4,6,4,9],[9,6,9,8],[10,6,10,8],[11,6,11,8],[12,6,12,8]]}
["UNIVARIATE GOMPERTZ"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Gompertz\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"(1/$H$7)*LN(1-(LN(1-$B4)/$H$8))","v":0.58144960989453098},{"$f":"gompertz($H$7,$H$8,$B4)","v":0.58144960989453098},{"$f":"gompertz($H$7,$H$8)","v":1.5836205372219467}]
[{"$f":"A4+1","v":2},0.79377423808874648,2.3275033420262834,2.3275033420262834,1.4218067459408059,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,2.4886035188710594,2.4886035188710594,0.8543935138022708,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,1.7455445553193623,1.7455445553193623,1.8683965120677803,null,"sigma = ",0.25,"Scale","Real number greater than zero"]
[5,0.86717342695468203,2.7912560594394655,2.7912560594394655,2.1755293475009192,null,"alpha = ",2,"Shape","Real number greater than zero"]
[6,0.27994300504477809,0.608179417291971,0.608179417291971,1.2394015272967134]
[7,0.93667220783619842,3.4679237637215032,3.4679237637215032,0.23075857234719088,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,0.99599079506422294,0.99599079506422294,0.34901536455758614,null,"Distrbution Name:",null,null,"Gompertz"]
[9,0.96203701528155405,3.8764007023654807,3.8764007023654807,2.1085613236300631,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,0.29601488137131382,0.29601488137131382,1.2913903848395669,null,"Simulation Method:",null,null,"Inverse Transform"]
[11,0.20171971836271319,0.42697016442134367,0.42697016442134367,3.1817042589523163]
[12,0.58041618261550787,1.4425570604531304,1.4425570604531304,0.19551272675071793,null,"Macro Format:",null,null,"=Gompertz(sigma, alpha, [unif])"]
[13,0.34366851316718994,0.76428153312115643,0.76428153312115643,0.21762706753553235]
[14,0.9651686825697714,3.9412057296252447,3.9412057296252447,5.9155164651233525,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[15,0.38704808829902526,0.87568868500353625,0.87568868500353625,3.17709695267849,null,null,null,null,"your own uniform random variable (unif). If"]
[16,0.86385756571325945,2.7666379283021456,2.7666379283021456,7.3458692590259731E-3,null,null,null,null,"not provided, the function will generate one"]
[17,0.17476282037902591,0.36682284514118374,0.36682284514118374,1.5245731087793553,null,null,null,null,"to be used within the macro."]
[18,0.38117659587117037,0.86034122549539993,0.86034122549539993,0.58409218933670903,null,null,null,null,"2. Column C shows the formula used in the"]
[19,0.87794506028866293,2.8745618024588739,2.8745618024588739,1.9074040672230086,null,null,null,null,"macro directly in the cell.  Column D generates"]
[20,0.18238019015349183,0.38370874050936354,0.38370874050936354,1.4902496835143735,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,0.90331652158380971,0.90331652158380971,1.4303521986226424,null,null,null,null,"same uniform random variable (column A) as"]
[22,0.74199757940000399,2.0689635816647076,2.0689635816647076,1.1761895047069382,null,null,null,null,"used in Column C, and therefore the output of"]
[23,0.57082894586967958,1.4109283209583419,1.4109283209583419,2.5158043540627797,null,null,null,null,"Columns C and D will match.  Column E runs"]
[24,0.90195869363590486,3.0826233939251817,3.0826233939251817,3.343772134894984,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,1.0139458018085619,1.0139458018085619,2.1654368990803676,null,null,null,null,"uniform random input."]
[26,0.3929492390413114,0.8912025548376078,0.8912025548376078,1.2260359317685225]
[27,0.2515715048326993,0.54123356971670533,0.54123356971670533,2.8149826584079189]
[28,0.30550021398012439,0.66978490396123136,0.66978490396123136,0.28250031949479204]
[29,7.9387447484473794E-2,0.1621025465303601,0.1621025465303601,2.0095605637396625]
[30,0.82057811417206794,2.4801713408044139,2.4801713408044139,0.5802091333278907]
[31,5.0767455327721533E-3,1.0166421505871706E-2,1.0166421505871706E-2,0.34048653232845494]
[32,2.9980457362279278E-2,6.0419500544392005E-2,6.0419500544392005E-2,1.8608825209983824]
[33,0.89698739215075429,{"$f":"(1/$H$7)*LN(1-(LN(1-$B36)/$H$8))","v":3.0365859356357983},3.0365859356357983,3.4721562910852493]
[34,4.8518018441997213E-2,9.8252425221031267E-2,9.8252425221031267E-2,0.24212195044515783]
[35,0.37123916516677757,0.83456248215593787,0.83456248215593787,0.52484105263545078]
[36,0.18273885825049341,0.38450593206215533,0.38450593206215533,3.8113942750045338]
[37,0.12050005291704391,0.24889670850510975,0.24889670850510975,0.34663578597475803]
[38,0.64945693361731327,1.6857103863655349,1.6857103863655349,2.9969590308981962E-2]
[39,0.84523354850406707,2.6361252473867891,2.6361252473867891,0.63508290055260386]
[40,0.96559113278394504,3.9503064878667562,3.9503064878667562,1.6334980569109974]
[41,0.66499232931154673,1.7447555148338501,1.7447555148338501,2.4070231064945151E-2]
[42,0.48716817186481609,1.1524388859208039,1.1524388859208039,2.6807377190925461]
[43,0.77210315614728597,2.2142324133704259,2.2142324133704259,0.2366707975185974]
[44,0.82636627627465631,2.5152955951937401,2.5152955951937401,1.4702092052677205]
[45,0.30996283637913491,0.68067507716171294,0.68067507716171294,2.062891922877363]
[46,0.1840653161997976,0.38745583659004224,0.38745583659004224,0.19001298115870796]
[47,0.58275788798882977,1.450353768623009,1.450353768623009,1.2901647968740475]
[48,0.3211056530871087,0.70804620879778168,0.70804620879778168,0.54028733937173745]
[49,0.94059973373021577,3.5213744847432769,3.5213744847432769,0.70299811150739289]
[50,0.14907620621989892,0.31049643955400236,0.31049643955400236,0.89101126498107797]
[51,0.38302044178353878,0.86515143716521259,0.86515143716521259,1.5336549485353943]
[52,8.4815952479745493E-2,0.17344484299844951,0.17344484299844951,1.2166626868016039]
[53,0.84221407414122895,2.6160825587504806,2.6160825587504806,2.0285525561465745]
[54,0.40498559499715014,0.92312867244619889,0.92312867244619889,0.27117427291494883]
[55,0.31192254229901473,0.6854702266552275,0.6854702266552275,2.0153277378451295]
[56,7.3945219604894419E-2,0.15076642479741253,0.15076642479741253,2.8892963362179929]
[57,0.41540561914582874,0.95108345591169674,0.95108345591169674,0.38163713783483688]
[58,0.94334481547755944,3.560420879163634,3.560420879163634,0.82912343866338278]
[59,0.6294690698059815,1.6122734266713961,1.6122734266713961,2.9947685009563192]
[60,0.21751765244325438,0.46273919399166885,0.46273919399166885,1.4128596529493198]
[61,0.81132182231923589,2.4256839376452488,2.4256839376452488,2.0708138153306539]
[62,0.47641953418452843,1.1212165186241578,1.1212165186241578,0.84389349099208377]
[63,0.92308615531225435,3.3011461297389015,3.3011461297389015,2.9006374721906791]
[64,0.62241658364570296,1.5869939328679896,1.5869939328679896,2.6031264896951019E-2]
[65,0.56290274788396399,{"$f":"(1/$H$7)*LN(1-(LN(1-$B68)/$H$8))","v":1.3851238418990466},1.3851238418990466,2.5516427028566868]
[66,0.27617460253729631,0.59920220587882445,{"$f":"gompertz($H$7,$H$8,$B69)","v":0.59920220587882445},{"$f":"gompertz($H$7,$H$8)","v":2.4755900898203294}]
[{"$f":"A69+1","v":67},0.98183097898545246,4.3998037539373325,4.3998037539373325,1.0009627902638161]
[68,0.17855864253016906,0.3752266162152606,0.3752266162152606,0.21392667477692917]
[69,0.14106716857892998,0.29312183396377339,0.29312183396377339,4.3472301021106174]
[70,0.78799892820694739,2.2965129682429191,2.2965129682429191,0.16012418383488661]
[71,0.62019869479720879,1.5791088406070013,1.5791088406070013,0.3152299531967872]
[72,0.32070616340267466,0.70706041972558697,0.70706041972558697,0.76769146771931707]
[73,0.71916827005391148,1.9665707462418685,1.9665707462418685,0.63423988705426093]
[74,0.70290736382840724,1.8971170060653602,1.8971170060653602,0.92877319709944239]
[75,0.154172834186179,0.32159870376584815,0.32159870376584815,0.43998461985601367]
[76,0.27977295388613965,0.6077737395113112,0.6077737395113112,1.3375575146692478]
[77,0.42321062277449939,0.97222094150730842,0.97222094150730842,2.6522117086115191]
[78,0.98136142771892321,4.3827801953155321,4.3827801953155321,4.027203116504325E-2]
[79,0.20085756040090119,0.42502939171141185,0.42502939171141185,1.4726024799254473]
[80,0.16133779816984994,0.33726766898722343,0.33726766898722343,1.0992710882257837]
[81,0.25863578352871763,0.55776626726482426,0.55776626726482426,0.57053682460611754]
[82,0.8347220398143228,2.5675488216847331,2.5675488216847331,1.7605234756942112]
[83,0.51591167107959424,1.2380010966068413,1.2380010966068413,2.8226667688823794]
[84,0.24633192212221666,0.52902796377675654,0.52902796377675654,4.6160222984007468]
[85,0.59063871388364364,1.476804690339748,1.476804690339748,1.2747217292664212]
[86,0.65393134749071002,1.7025322510615235,1.7025322510615235,0.11634176522205927]
[87,0.56445460206933995,1.3901520590039331,1.3901520590039331,0.32901974831460018]
[88,0.10565266639072934,0.21731076333438556,0.21731076333438556,3.7268386465117804]
[89,0.59226465879030998,1.4823032938473943,1.4823032938473943,0.47247982524162357]
[90,0.72089126375496948,1.9740917730187526,1.9740917730187526,0.52458669971939986]
[91,0.58803803186325454,1.4680393597229009,1.4680393597229009,1.2438167077696523]
[92,0.76602838211191659,2.1838699597207203,2.1838699597207203,1.7729863272016921]
[93,0.48285856602942256,1.1398718832493686,1.1398718832493686,2.6590202223834165]
[94,0.62864718503333628,1.6093110130605073,1.6093110130605073,0.53663711536248693]
[95,0.33779794281158637,0.74954243006459187,0.74954243006459187,5.3814187147383598E-2]
[96,0.47576831339143399,1.1193377542062801,1.1193377542062801,1.4717186672255773]
[97,5.6312473117793416E-2,0.11427242586403842,0.11427242586403842,0.26157511339111922]
[98,0.80804733641082538,2.4068749574756265,2.4068749574756265,1.5918007328880663]
[99,0.49894266970018275,1.1871144220912349,1.1871144220912349,0.15802743156981683]
[100,0.32081795804802316,0.70733625257109212,0.70733625257109212,1.8505026139761691]

{"sheet":"Gumbel","index":14,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,6,14,8],[4,6,4,9],[0,0,0,5],[9,6,9,8],[10,6,10,8],[11,6,11,8],[12,6,12,8]]}
["UNIVARIATE GUMBEL"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Gumbel\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7-$H$8*LN(-LN($B4))","v":0.9070914526351963},{"$f":"gumbel($H$7,$H$8,$B4)","v":0.9070914526351963},{"$f":"gumbel($H$7,$H$8)","v":1.2058765291489961}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7-$H$8*LN(-LN($B5))","v":7.8621089073937735},7.8621089073937735,-1.956323400399103,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,8.5177709805517345,8.5177709805517345,2.5143627703564144,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,5.5891649129531373,5.5891649129531373,1.2172641972750424,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,9.793195848760007,9.793195848760007,11.927106828549253,null,"sigma = ",4,"Scale","Real number greater than zero"]
[6,0.27994300504477809,1.0339629426132868,1.0339629426132868,6.4337262558700861]
[7,0.93667220783619842,12.907593498700699,12.907593498700699,1.5914514787780032,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,2.6996311082440267,2.6996311082440267,1.9406135246605367,null,"Distrbution Name:",null,null,"Gumbel"]
[9,0.96203701528155405,15.007419660326343,15.007419660326343,1.7464443620326202,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,-0.66945116845040165,-0.66945116845040165,-4.1146162808342908,null,"Simulation Method:",null,null,"Inverse Transform"]
[11,0.20171971836271319,0.11779588753277292,0.11779588753277292,2.168666721707214]
[12,0.58041618261550787,4.4351515076314705,4.4351515076314705,0.43962682925164098,null,"Macro Format:",null,null,"=Gumbel(mu, sigma, [unif])"]
[13,0.34366851316718994,1.7365579970981166,1.7365579970981166,4.5202078457347268]
[14,0.9651686825697714,15.358258174781756,15.358258174781756,1.5865517978751407,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[15,0.38704808829902526,2.2085163237076433,2.2085163237076433,1.5857352296849734,null,null,null,null,"your own uniform random variable (unif). If"]
[16,0.86385756571325945,9.6870887205512268,9.6870887205512268,4.78305016235994,null,null,null,null,"not provided, the function will generate one"]
[17,0.17476282037902591,-0.22547187549294945,-0.22547187549294945,12.442159453882885,null,null,null,null,"to be used within the macro."]
[18,0.38117659587117037,2.1446128700556306,2.1446128700556306,3.0520552330921777,null,null,null,null,"2. Column C shows the formula used in the"]
[19,0.87794506028866293,10.155617212630553,10.155617212630553,4.4387746341887819,null,null,null,null,"macro directly in the cell.  Column D generates"]
[20,0.18238019015349183,-0.12642124458014514,-0.12642124458014514,6.3672210585725351,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,2.322773753606092,2.322773753606092,0.57190857168733222,null,null,null,null,"same uniform random variable (column A) as"]
[22,0.74199757940000399,6.8371570053532471,6.8371570053532471,8.3492892836564678,null,null,null,null,"used in Column C, and therefore the output of"]
[23,0.57082894586967958,4.3145219219515276,4.3145219219515276,18.54162600732721,null,null,null,null,"Columns C and D will match.  Column E runs"]
[24,0.90195869363590486,11.084866894152348,11.084866894152348,-1.0639529345803971,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,2.771651351582479,2.771651351582479,2.7523370782020402,null,null,null,null,"uniform random input."]
[26,0.3929492390413114,2.2727948696437865,2.2727948696437865,17.216252893524054]
[27,0.2515715048326993,0.71158479718653433,0.71158479718653433,1.5851180667192004]
[28,0.30550021398012439,1.3183131994538684,1.3183131994538684,2.3718199396215103]
[29,7.9387447484473794E-2,-1.7182728040417743,-1.7182728040417743,14.29051731331546]
[30,0.82057811417206794,8.4830841647018929,8.4830841647018929,3.2791498644957713]
[31,5.0767455327721533E-3,-4.6580407280114828,-4.6580407280114828,3.4874729290314668]
[32,2.9980457362279278E-2,-3.0192828633435882,-3.0192828633435882,3.6592807476718008]
[33,0.89698739215075429,10.876158198460589,10.876158198460589,3.0416254301851717]
[34,4.8518018441997213E-2,-2.4287285637956106,-2.4287285637956106,-2.264391259466545]
[35,0.37123916516677757,2.0365312134101043,2.0365312134101043,10.286265428693181]
[36,0.18273885825049341,-0.12180035106550813,-0.12180035106550813,4.1963910481404199]
[37,0.12050005291704391,-0.99830870304763719,-0.99830870304763719,2.0113280603463597]
[38,0.64945693361731327,5.3608503951705284,5.3608503951705284,11.588500456120443]
[39,0.84523354850406707,9.1317785121615351,9.1317785121615351,4.0384182094337584E-2]
[40,0.96559113278394504,15.407938672123137,15.407938672123137,-3.6281709962467268E-2]
[41,0.66499232931154673,5.5861507245739173,5.5861507245739173,3.3479188012760814]
[42,0.48716817186481609,3.3187641211754837,3.3187641211754837,12.687103572860378]
[43,0.77210315614728597,7.4093171861037019,7.4093171861037019,1.3919656459405232]
[44,0.82636627627465631,8.6278549348397817,8.6278549348397817,3.2208843793218778]
[45,0.30996283637913491,1.3675332219943037,1.3675332219943037,5.9135930741421889]
[46,0.1840653161997976,-0.10474325097865433,-0.10474325097865433,1.3101046258045923]
[47,0.58275788798882977,4.4648670384185065,4.4648670384185065,3.0229976823650837]
[48,0.3211056530871087,1.4899992801955666,1.4899992801955666,4.713464936880376]
[49,0.94059973373021577,13.171976082349758,13.171976082349758,0.6858447601903177]
[50,0.14907620621989892,-0.57435195360734737,-0.57435195360734737,8.4345469596589346]
[51,0.38302044178353878,2.1646760588041953,2.1646760588041953,6.1465172842825462]
[52,8.4815952479745493E-2,-1.6124517556336673,-1.6124517556336673,-3.031712956843255]
[53,0.84221407414122895,9.0475356321837008,9.0475356321837008,1.5608447828310736]
[54,0.40498559499715014,2.4041294473891859,2.4041294473891859,12.211475372671329]
[55,0.31192254229901473,1.3891143339660781,1.3891143339660781,2.2019826672277891]
[56,7.3945219604894419E-2,-1.8288564947832731,-1.8288564947832731,8.1820601132423292]
[57,0.41540561914582874,2.5181582113877861,2.5181582113877861,2.4749642498857156]
[58,0.94334481547755944,13.367007218947682,13.367007218947682,-1.309874048198544]
[59,0.6294690698059815,5.0811621840939036,5.0811621840939036,-0.6433549925224531]
[60,0.21751765244325438,0.31077594128743669,0.31077594128743669,1.7493017446944794]
[61,0.81132182231923589,8.2599527703251692,8.2599527703251692,11.265696488156424]
[62,0.47641953418452843,3.1965554672368555,3.1965554672368555,13.783984826442767]
[63,0.92308615531225435,12.101279604656646,12.101279604656646,10.222984338085531]
[64,0.62241658364570296,4.9849628044955079,4.9849628044955079,4.832752258090145E-2]
[65,0.56290274788396399,4.2159875800109212,4.2159875800109212,1.8684355274538689]
[66,0.27617460253729631,{"$f":"$H$7-$H$8*LN(-LN($B69))","v":0.99160841805564037},{"$f":"gumbel($H$7,$H$8,$B69)","v":0.99160841805564037},{"$f":"gumbel($H$7,$H$8)","v":7.2027959402034938}]
[{"$f":"A69+1","v":67},0.98183097898545246,17.995532935083641,17.995532935083641,1.6555990563257754]
[68,0.17855864253016906,-0.17589219359215846,-0.17589219359215846,2.1439039996968958]
[69,0.14106716857892998,-0.68875456525146372,-0.68875456525146372,9.8584142855468855]
[70,0.78799892820694739,7.7375954139505456,7.7375954139505456,-0.74460968562817431]
[71,0.62019869479720879,4.9549606794154313,4.9549606794154313,-1.2804501318771759]
[72,0.32070616340267466,1.4856182381137133,1.4856182381137133,16.283334770228457]
[73,0.71916827005391148,6.438774863800691,6.438774863800691,5.8830053305398113]
[74,0.70290736382840724,6.1704763039528245,6.1704763039528245,-2.5934826595337679]
[75,0.154172834186179,-0.50307132508115648,-0.50307132508115648,11.594819400405916]
[76,0.27977295388613965,1.0320543547858689,1.0320543547858689,2.5668887001046841]
[77,0.42321062277449939,2.6038250936860741,2.6038250936860741,1.238988609851283]
[78,0.98136142771892321,17.892518346380722,17.892518346380722,20.56350061894917]
[79,0.20085756040090119,0.10710804169260912,0.10710804169260912,-1.8927939695070353]
[80,0.16133779816984994,-0.40468670890839453,-0.40468670890839453,-1.9470041784794825]
[81,0.25863578352871763,0.79267072025754293,0.79267072025754293,4.4588874361854707]
[82,0.8347220398143228,8.8446314519885902,8.8446314519885902,-7.0253992688430689E-2]
[83,0.51591167107959424,3.6510484167925554,3.6510484167925554,-1.0479144186353109]
[84,0.24633192212221666,0.651039731269347,0.651039731269347,13.206070608456439]
[85,0.59063871388364364,4.5656301540548609,4.5656301540548609,8.4982052691656946]
[86,0.65393134749071002,5.4249907043890744,5.4249907043890744,-1.4491635212386114]
[87,0.56445460206933995,4.2351972445640431,4.2351972445640431,2.9898286359279389]
[88,0.10565266639072934,-1.2394488907254955,-1.2394488907254955,4.2153161483902508]
[89,0.59226465879030998,4.5865685183786429,4.5865685183786429,-0.45721205270572218]
[90,0.72089126375496948,6.4679161234362805,6.4679161234362805,5.9230656926495993]
[91,0.58803803186325454,4.5322468396869704,4.5322468396869704,3.906103059960869]
[92,0.76602838211191659,7.2889829764248821,7.2889829764248821,12.017319396115941]
[93,0.48285856602942256,3.2696438930023248,3.2696438930023248,5.429984343567325]
[94,0.62864718503333628,5.0698875894257451,5.0698875894257451,11.972764655684887]
[95,0.33779794281158637,1.6725470711674824,1.6725470711674824,-0.63772414048262682]
[96,0.47576831339143399,3.189183052611948,3.189183052611948,3.567861537929339]
[97,5.6312473117793416E-2,-2.2267687949985282,-2.2267687949985282,1.3786073802416179]
[98,0.80804733641082538,8.1833248479102902,8.1833248479102902,5.5070070825224535]
[99,0.49894266970018275,3.4538541362440913,3.4538541362440913,0.74791124637196305]
[100,0.32081795804802316,1.4868443109509168,1.4868443109509168,-0.68679902130679737]

{"sheet":"Laplace","index":15,"n_rows":103,"n_cols":11,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,7,14,9],[0,0,0,5],[4,7,4,10],[9,7,9,9],[10,7,10,9],[11,7,11,9],[12,7,12,9]]}
["UNIVARIATE LAPLACE"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate (0,1)","Uniform\nRandom\nVariate\n(-1/2, 1/2)","LaPlace\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"-1/2+1*B4","v":-0.23131046579839576},{"$f":"$I$7-$I$8*SIGN($C4)*LN(1-2*ABS($C4))","v":-0.24210306662286318},{"$f":"laplace($I$7,$I$8,$B4)","v":-0.24210306662286318},{"$f":"laplace($I$7,$I$8)","v":-1.2179493094918823}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"-1/2+1*B5","v":0.29377423808874648},{"$f":"$I$7-$I$8*SIGN($C5)*LN(1-2*ABS($C5))","v":2.7712731962384538},2.7712731962384538,-0.2164587629672734,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.32198035169288064,3.0654283409481651,3.0654283409481651,-1.451353580809851,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.16519672361232263,1.8021299475011627,1.8021299475011627,1.8254676860882872,null,"mu = ",1,"Location","Any finite real number"]
[5,0.86717342695468203,0.36717342695468203,3.6511275663280469,3.6511275663280469,-3.1246302729921664,null,"sigma = ",2,"Scale","Real number greater than zero"]
[6,0.27994300504477809,-0.22005699495522191,-0.16004413876851276,-0.16004413876851276,1.9306097394952151]
[7,0.93667220783619842,0.43667220783619842,5.1325676218159559,5.1325676218159559,-1.9933450779124104,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,-6.8088443288595313E-2,0.70722547805438762,0.70722547805438762,3.645848473776033,null,"Distrbution Name:",null,null,"LaPlace"]
[9,0.96203701528155405,0.46203701528155405,6.1559929995658349,6.1559929995658349,1.8733571999584004,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,-0.35759645424066488,-1.5118863995179703,-1.5118863995179703,8.2213430747911946,null,"Simulation Method:",null,null,"Inverse Transform"]
[11,0.20171971836271319,-0.29828028163728681,-0.81545779478786806,-0.81545779478786806,3.2184820147613871]
[12,0.58041618261550787,8.041618261550787E-2,1.3506895788218889,1.3506895788218889,3.753120112220262,null,"Macro Format:",null,null,"=Laplace(mu, sigma, [unif])"]
[13,0.34366851316718994,-0.15633148683281006,0.25013893970528234,0.25013893970528234,1.4733001584533425]
[14,0.9651686825697714,0.4651686825697714,6.3281823803530708,6.3281823803530708,-3.8410314412841107,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[15,0.38704808829902526,-0.11295191170097474,0.48788169211733345,0.48788169211733345,1.7961595497986247,null,null,null,null,"your own uniform random variable (unif). If"]
[16,0.86385756571325945,0.36385756571325945,3.6018128996034013,3.6018128996034013,1.1378325989600491,null,null,null,null,"not provided, the function will generate one"]
[17,0.17476282037902591,-0.32523717962097409,-1.1023567117693793,-1.1023567117693793,-0.55039563524434953,null,null,null,null,"to be used within the macro."]
[18,0.38117659587117037,-0.11882340412882963,0.45730935108445048,0.45730935108445048,1.0203352315444369,null,null,null,null,"2. Column D shows the formula used in the"]
[19,0.87794506028866293,0.37794506028866293,3.8202736591045414,3.8202736591045414,1.6545181309917396,null,null,null,null,"macro directly in the cell.  Column E generates"]
[20,0.18238019015349183,-0.31761980984650817,-1.0170292665894287,-1.0170292665894287,-3.0736967010830414,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,-0.10246664798014993,0.54134147320973236,0.54134147320973236,0.30690386654045065,null,null,null,null,"same uniform random variable (column C) as"]
[22,0.74199757940000399,0.24199757940000399,2.323278262748119,2.323278262748119,6.7107011040954747,null,null,null,null,"used in Column D, and therefore the output of"]
[23,0.57082894586967958,7.0828945869679583E-2,1.3055050627767728,1.3055050627767728,0.63791795956106467,null,null,null,null,"Columns D and E will match.  Column F runs"]
[24,0.90195869363590486,0.40195869363590486,4.2584384300877645,4.2584384300877645,1.4364098305512594,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,-6.1569441361920219E-2,0.7371866794099321,0.7371866794099321,6.5803706837462181,null,null,null,null,"uniform random input.  Note that Column C is"]
[26,0.3929492390413114,-0.1070507609586886,0.51814468472017827,0.51814468472017827,0.48369553459970493,null,null,null,null,"a necessary transform of the uniform random"]
[27,0.2515715048326993,-0.2484284951673007,-0.37376167168342223,-0.37376167168342223,-3.8209619685156309,null,null,null,null,"variable in Column B."]
[28,0.30550021398012439,-0.19449978601987561,1.4684761230304155E-2,1.4684761230304155E-2,-1.0110814811688158]
[29,7.9387447484473794E-2,-0.42061255251552621,-2.6805356696041427,-2.6805356696041427,-2.5229635248720257]
[30,0.82057811417206794,0.32057811417206794,3.0497363233133377,3.0497363233133377,-5.5371729396937814]
[31,5.0767455327721533E-3,-0.49492325446722785,-8.1798753705728053,-8.1798753705728053,0.79660506488541794]
[32,2.9980457362279278E-2,-0.47001954263772072,-4.6281247005688186,-4.6281247005688186,4.3881451371953517]
[33,0.89698739215075429,0.39698739215075429,4.1595134227604795,4.1595134227604795,0.47023337820867472]
[34,4.8518018441997213E-2,-0.45148198155800279,-3.6653457104102172,-3.6653457104102172,-6.2795776297600359E-2]
[35,0.37123916516677757,-0.12876083483322243,0.40447681306576455,0.40447681306576455,-1.0742260504553074]
[36,0.18273885825049341,-0.31726114174950659,-1.0130999376328798,-1.0130999376328798,1.1880731447116881]
[37,0.12050005291704391,-0.37949994708295609,-1.8459158126919717,-1.8459158126919717,0.91635137665304622]
[38,0.64945693361731327,0.14945693361731327,1.7102490564366475,1.7102490564366475,-0.79844631062816762]
[39,0.84523354850406707,0.34523354850406707,3.3453817647131712,3.3453817647131712,-0.84102928419206768]
[40,0.96559113278394504,0.46559113278394504,6.3525875987014082,6.3525875987014082,1.2706089635615561]
[41,0.66499232931154673,0.16499232931154673,1.8009093385635966,1.8009093385635966,2.6947941743507093]
[42,0.48716817186481609,-1.2831828135183909E-2,0.94800257430957602,0.94800257430957602,0.87073806351784677]
[43,0.77210315614728597,0.27210315614728597,2.5714300221834989,2.5714300221834989,2.1124593902211175]
[44,0.82636627627465631,0.32636627627465631,3.1153201079429897,3.1153201079429897,1.3487620427504881]
[45,0.30996283637913491,-0.19003716362086509,4.3688618445098526E-2,4.3688618445098526E-2,-1.7344425979014817]
[46,0.1840653161997976,-0.3159346838002024,-0.99863484891348397,-0.99863484891348397,-0.44796744197462579]
[47,0.58275788798882977,8.275788798882977E-2,1.3618828815310915,1.3618828815310915,0.74982909339143644]
[48,0.3211056530871087,-0.1788943469128913,0.11432421579405794,0.11432421579405794,-2.7174847634148049]
[49,0.94059973373021577,0.44059973373021577,5.2606187788146785,5.2606187788146785,-1.2202047007680856]
[50,0.14907620621989892,-0.35092379378010108,-1.4203009441660548,-1.4203009441660548,0.7976705744870124]
[51,0.38302044178353878,-0.11697955821646122,0.46696052427430035,0.46696052427430035,1.9005439755146472]
[52,8.4815952479745493E-2,-0.41518404752025451,-2.548248908903092,-2.548248908903092,1.1670455461341822]
[53,0.84221407414122895,0.34221407414122895,3.3067377674593756,3.3067377674593756,0.32285848765491043]
[54,0.40498559499715014,-9.5014405002849855E-2,0.57848680028704624,0.57848680028704624,-2.7236279377984687]
[55,0.31192254229901473,-0.18807745770098527,5.629359340616169E-2,5.629359340616169E-2,1.9196960113225119]
[56,7.3945219604894419E-2,-0.42605478039510558,-2.8225671099336935,-2.8225671099336935,2.5787249459908241]
[57,0.41540561914582874,-8.4594380854171258E-2,0.62929468000123778,0.62929468000123778,1.3916494875075349]
[58,0.94334481547755944,0.44334481547755944,5.3552491932921091,5.3552491932921091,1.219101281064229]
[59,0.6294690698059815,0.1294690698059815,1.5993423497309214,1.5993423497309214,-2.6111842822684843]
[60,0.21751765244325438,-0.28248234755674562,-0.66465618105632029,-0.66465618105632029,0.19399421252110516]
[61,0.81132182231923589,0.31132182231923589,2.9491305966121786,2.9491305966121786,3.0722690889941977]
[62,0.47641953418452843,-2.3580465815471574E-2,0.90338148392836837,0.90338148392836837,-15.550453795119189]
[63,0.92308615531225435,0.42308615531225435,4.7438444063275238,4.7438444063275238,-0.57725654681314431]
[64,0.62241658364570296,0.12241658364570296,1.5616331673370656,1.5616331673370656,-2.8991127345123529]
[65,0.56290274788396399,6.2902747883963994E-2,1.2689047663961752,1.2689047663961752,-0.38754979046355809]
[66,0.27617460253729631,{"$f":"-1/2+1*B69","v":-0.22382539746270369},{"$f":"$I$7-$I$8*SIGN($C69)*LN(1-2*ABS($C69))","v":-0.18714962966926252},{"$f":"laplace($I$7,$I$8,$B69)","v":-0.18714962966926252},{"$f":"laplace($I$7,$I$8)","v":-1.5642662844237258}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.48183097898545246,7.6297801933740574,7.6297801933740574,1.5258459989977788]
[68,0.17855864253016906,-0.32144135746983094,-1.0593820431514898,-1.0593820431514898,0.66509739225238707]
[69,0.14106716857892998,-0.35893283142107002,-1.5307438971467184,-1.5307438971467184,3.1153753681120095]
[70,0.78799892820694739,0.28799892820694739,2.7160335362707047,2.7160335362707047,0.62186764714561193]
[71,0.62019869479720879,0.12019869479720879,1.5499197269940235,1.5499197269940235,-3.9250219619122486]
[72,0.32070616340267466,-0.17929383659732534,0.11183445336985898,0.11183445336985898,0.49381216999413247]
[73,0.71916827005391148,0.21916827005391148,2.1537048685417322,2.1537048685417322,6.3298002772142263]
[74,0.70290736382840724,0.20290736382840724,2.0411282039009824,2.0411282039009824,6.0510300881510686]
[75,0.154172834186179,-0.345827165813821,-1.3530676508120991,-1.3530676508120991,8.3259568119683802]
[76,0.27977295388613965,-0.22022704611386035,-0.16125940634241154,-0.16125940634241154,-2.8398265449099425]
[77,0.42321062277449939,-7.678937722550061E-2,0.66652376576166006,0.66652376576166006,-5.9387387352524579E-2]
[78,0.98136142771892321,0.48136142771892321,7.5787497729221549,7.5787497729221549,-1.8728160078532872]
[79,0.20085756040090119,-0.29914243959909881,-0.82402419259889581,-0.82402419259889581,-0.24404477454112428]
[80,0.16133779816984994,-0.33866220183015006,-1.2622156123001935,-1.2622156123001935,4.7799371644361663]
[81,0.25863578352871763,-0.24136421647128237,-0.31837453521921621,-0.31837453521921621,-0.42643214204636815]
[82,0.8347220398143228,0.3347220398143228,3.2139588693896037,3.2139588693896037,-8.5729836769901748]
[83,0.51591167107959424,1.5911671079594236E-2,1.0646814211736375,1.0646814211736375,-1.140319757987093]
[84,0.24633192212221666,-0.25366807787778334,-0.41585639005274344,-0.41585639005274344,-3.4102193746186726]
[85,0.59063871388364364,9.063871388364364E-2,1.4000199843137944,1.4000199843137944,6.8909931339715733]
[86,0.65393134749071002,0.15393134749071002,1.7359418507794797,1.7359418507794797,2.0589529414601309]
[87,0.56445460206933995,6.445460206933995E-2,1.2760181286468193,1.2760181286468193,1.5009735884578972]
[88,0.10565266639072934,-0.39434733360927066,-2.1089022334323624,-2.1089022334323624,3.0881249481609334]
[89,0.59226465879030998,9.2264658790309984E-2,1.4079796160067537,1.4079796160067537,-1.9051029611955661]
[90,0.72089126375496948,0.22089126375496948,2.16601331376553,2.16601331376553,1.8250163602537044]
[91,0.58803803186325454,8.803803186325454E-2,1.3873541273624659,1.3873541273624659,1.5951198025078486]
[92,0.76602838211191659,0.26602838211191659,2.5188165629948287,2.5188165629948287,2.4850312108372297]
[93,0.48285856602942256,-1.7141433970577435E-2,0.93023137678685652,0.93023137678685652,1.3044388563744502]
[94,0.62864718503333628,0.12864718503333628,1.594911007951354,1.594911007951354,0.67020893819956262]
[95,0.33779794281158637,-0.16220205718841363,0.21567963194636852,0.21567963194636852,1.470366436590536]
[96,0.47576831339143399,-2.4231686608566005E-2,0.900645801483826,0.900645801483826,1.6333461281259214]
[97,5.6312473117793416E-2,-0.44368752688220658,-3.3673840808584536,-3.3673840808584536,-1.2298994714253069]
[98,0.80804733641082538,0.30804733641082538,2.9147186011954256,2.9147186011954256,10.34135621990051]
[99,0.49894266970018275,-1.0573302998172496E-3,0.99576620069705268,0.99576620069705268,0.45600039136528936]
[100,0.32081795804802316,-0.17918204195197684,0.11253150991219041,0.11253150991219041,-0.50905255878820754]

{"sheet":"Logistic","index":16,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,6,14,8],[0,0,0,5],[4,6,4,9],[9,6,9,8],[10,6,10,8],[11,6,11,8],[12,6,12,8]]}
["UNIVARIATE LOGISTIC"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Logistic\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7+$H$8*LN($B4/(1-$B4))","v":-2.0051260731525193},{"$f":"Logistic($H$7,$H$8,$B4)","v":-2.0051260731525193},{"$f":"Logistic($H$7,$H$8)","v":-1.309898652309609}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7+$H$8*LN($B5/(1-$B5))","v":7.3913103424500628},7.3913103424500628,-2.0492694212913092,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,8.1192902550894601,8.1192902550894601,7.2715388169937674,null,"Name","Value","Type","Feasible Range"]
[{"$f":"A6+1","v":4},0.66519672361232263,4.7461587888703916,4.7461587888703916,10.566249249535577,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,9.5047786904336853,9.5047786904336853,15.350806443768731,null,"sigma = ",4,"Scale","Real number greater than zero"]
[6,0.27994300504477809,-1.7789773579969421,-1.7789773579969421,9.7181410355826898]
[7,0.93667220783619842,12.776036407869309,12.776036407869309,2.8754125033855678,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,0.9037748833385908,0.9037748833385908,11.953511177677404,null,"Distrbution Name:",null,null,"Logistic"]
[9,0.96203701528155405,14.929765314839392,14.929765314839392,5.5317209887446595E-2,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,-5.1818750285225352,-5.1818750285225352,15.379970006129414,null,"Simulation Method:",null,null,"Inverse Transform"]
[11,0.20171971836271319,-3.5023222595064158,-3.5023222595064158,-8.3267058349340317]
[12,0.58041618261550787,3.2979283737698601,3.2979283737698601,-1.4421690043323587,null,"Macro Format:",null,null,"=Logistic(mu, sigma, [unif])"]
[13,0.34366851316718994,-0.58795363333757589,-0.58795363333757589,-4.1936828813317133]
[14,0.9651686825697714,15.287143913631693,15.287143913631693,-6.2980722388712351,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[15,0.38704808829902526,0.16104983636668968,0.16104983636668968,-13.810107204807522,null,null,null,null,"your own uniform random variable (unif). If"]
[16,0.86385756571325945,9.3908250083801033,9.3908250083801033,10.473651975302015,null,null,null,null,"not provided, the function will generate one"]
[17,0.17476282037902591,-4.2089643717175358,-4.2089643717175358,-2.017335552068622,null,null,null,null,"to be used within the macro."]
[18,0.38117659587117037,6.1771336729459447E-2,6.1771336729459447E-2,4.3907498614555101,null,null,null,null,"2. Column C shows the formula used in the"]
[19,0.87794506028866293,9.8924509964170504,9.8924509964170504,18.210334103904493,null,null,null,null,"macro directly in the cell.  Column D generates"]
[20,0.18238019015349183,-4.0012159331710357,-4.0012159331710357,7.5203805503590448,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,0.33698610897597669,0.33698610897597669,-0.21154793830084406,null,null,null,null,"same uniform random variable (column A) as"]
[22,0.74199757940000399,6.2255080553991258,6.2255080553991258,6.2294996766074799,null,null,null,null,"used in Column C, and therefore the output of"]
[23,0.57082894586967958,3.1409361133488507,3.1409361133488507,-1.2904990459272918,null,null,null,null,"Columns C and D will match.  Column E runs"]
[24,0.90195869363590486,10.876719365762003,10.876719365762003,-7.5708248799399112,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,1.0098640017014819,1.0098640017014819,-11.654038897414544,null,null,null,null,"uniform random input."]
[26,0.3929492390413114,0.26027210903057107,0.26027210903057107,10.713413557748733]
[27,0.2515715048326993,-2.3609936235089259,-2.3609936235089259,7.2885791994816786]
[28,0.30550021398012439,-1.2849655002011064,-1.2849655002011064,26.196882859444326]
[29,7.9387447484473794E-2,-7.8027960112647659,-7.8027960112647659,-0.47215371182557409]
[30,0.82057811417206794,8.081076689471395,8.081076689471395,2.0048398290043394]
[31,5.0767455327721533E-3,-19.111980759437298,-19.111980759437298,-0.54714412666235068]
[32,2.9980457362279278E-2,-11.907081880823576,-11.907081880823576,2.8678070587720139]
[33,0.89698739215075429,10.656761677379075,10.656761677379075,-1.3727063486411528]
[34,4.8518018441997213E-2,-9.9043420258364172,-9.9043420258364172,6.5376967801457333]
[35,0.37123916516677757,-0.10761779459808407,-0.10761779459808407,-16.764733942574463]
[36,0.18273885825049341,-3.9916021965048056,-3.9916021965048056,7.2007532188459136]
[37,0.12050005291704391,-5.9508132477368596,-5.9508132477368596,-15.624496678138264]
[38,0.64945693361731327,4.4666118269185962,4.4666118269185962,0.97170817513109742]
[39,0.84523354850406707,8.7907830474617583,8.7907830474617583,6.2345676146443525]
[40,0.96559113278394504,15.337704750217801,15.337704750217801,0.73852908530573091]
[41,0.66499232931154673,4.7424883063163161,4.7424883063163161,-7.5639927744128421]
[42,0.48716817186481609,1.79464565820126,1.79464565820126,0.76968141079237284]
[43,0.77210315614728597,6.8809003028806366,6.8809003028806366,6.8835749583150916]
[44,0.82636627627465631,8.2403602581165991,8.2403602581165991,9.4017405067341073]
[45,0.30996283637913491,-1.2011721952649737,-1.2011721952649737,0.95569344764182329]
[46,0.1840653161997976,-3.9561745337297562,-3.9561745337297562,6.0892523530040892]
[47,0.58275788798882977,3.3364206238799206,3.3364206238799206,6.2178839134593327]
[48,0.3211056530871087,-0.99478123248175976,-0.99478123248175976,6.3678285959287235]
[49,0.94059973373021577,13.04887590964408,13.04887590964408,13.66327849081954]
[50,0.14907620621989892,-4.9674597967995933,-4.9674597967995933,-2.9909777748979627]
[51,0.38302044178353878,9.3009872529423721E-2,9.3009872529423721E-2,-10.589872275012064]
[52,8.4815952479745493E-2,-7.5145661836353828,-7.5145661836353828,-11.041020674086637]
[53,0.84221407414122895,8.6991800482335879,8.6991800482335879,-0.13909278055398788]
[54,0.40498559499715014,0.46106353289728474,0.46106353289728474,-2.1301798549860544]
[55,0.31192254229901473,-1.164586081354777,-1.164586081354777,1.234210340130129]
[56,7.3945219604894419E-2,-8.110435390140518,-8.110435390140518,-12.37690709002616]
[57,0.41540561914582874,0.63334879096647412,0.63334879096647412,-8.9809528763164987]
[58,0.94334481547755944,13.249793488013193,13.249793488013193,-4.4468937590502806]
[59,0.6294690698059815,4.1197591767152026,4.1197591767152026,4.0470597325926461]
[60,0.21751765244325438,-3.1207654209316198,-3.1207654209316198,9.6253419788241565]
[61,0.81132182231923589,7.8344879875538327,7.8344879875538327,1.5516619436680574]
[62,0.47641953418452843,1.6224324580146163,1.6224324580146163,-12.549753210839825]
[63,0.92308615531225435,11.940146710353721,11.940146710353721,-7.6838730444341046]
[64,0.62241658364570296,3.9992724097221299,3.9992724097221299,-2.5862221381154757]
[65,0.56290274788396399,3.0118046355584362,3.0118046355584362,-4.5004201149328269]
[66,0.27617460253729631,{"$f":"$H$7+$H$8*LN($B69/(1-$B69))","v":-1.8540676639518439},{"$f":"Logistic($H$7,$H$8,$B69)","v":-1.8540676639518439},{"$f":"Logistic($H$7,$H$8)","v":8.3559228674375241}]
[{"$f":"A69+1","v":67},0.98183097898545246,17.958804690582731,17.958804690582731,3.8657259932373003]
[68,0.17855864253016906,-4.1045738935357576,-4.1045738935357576,-0.83447470910614774]
[69,0.14106716857892998,-5.2258183006247911,-5.2258183006247911,13.45982392083773]
[70,0.78799892820694739,7.2516215977065874,7.2516215977065874,3.2405298760859216]
[71,0.62019869479720879,3.9615666690081146,3.9615666690081146,-11.104155889870597]
[72,0.32070616340267466,-1.0021138315259419,-1.0021138315259419,-2.9139686548267054]
[73,0.71916827005391148,5.761358798571357,5.761358798571357,6.4571237743979228]
[74,0.70290736382840724,5.4447244560324677,5.4447244560324677,7.3802896658125086]
[75,0.154172834186179,-4.8089630799620888,-4.8089630799620888,-4.3694977504014316]
[76,0.27977295388613965,-1.7823524354965521,-1.7823524354965521,-5.2782640544625101]
[77,0.42321062277449939,0.76157124895963646,0.76157124895963646,9.2892532785660471]
[78,0.98136142771892321,17.854830430397641,17.854830430397641,6.5260583703546766]
[79,0.20085756040090119,-3.523772800376813,-3.523772800376813,-1.0709509832703299]
[80,0.16133779816984994,-4.5932308525360783,-4.5932308525360783,-6.7425311508746919]
[81,0.25863578352871763,-2.2122847757247017,-2.2122847757247017,0.8450039669724887]
[82,0.8347220398143228,8.4778804770182372,8.4778804770182372,2.9221823715222071]
[83,0.51591167107959424,2.2546727316596091,2.2546727316596091,2.1853883721150056]
[84,0.24633192212221666,-2.4730886106914305,-2.4730886106914305,-10.894851582121047]
[85,0.59063871388364364,3.466425643948174,3.466425643948174,2.3468595971110924]
[86,0.65393134749071002,4.5454607986354958,4.5454607986354958,-8.9624932549770975]
[87,0.56445460206933995,3.0370436990709662,3.0370436990709662,8.7897298614967703]
[88,0.10565266639072934,-6.5437489374241533,-6.5437489374241533,4.7476188556286694]
[89,0.59226465879030998,3.4933412133264357,3.4933412133264357,1.3412618292530674]
[90,0.72089126375496948,5.7955474850887185,5.7955474850887185,3.0360003311381152]
[91,0.58803803186325454,3.4234423644222121,3.4234423644222121,4.7001549581006046]
[92,0.76602838211191659,6.7440776179792739,6.7440776179792739,-4.3112636360939316]
[93,0.48285856602942256,1.7256295321819977,1.7256295321819977,19.677506543578485]
[94,0.62864718503333628,4.1056703631452756,4.1056703631452756,-4.494935274224332E-2]
[95,0.33779794281158637,-0.69249126923905413,-0.69249126923905413,-2.1575522071818698]
[96,0.47576831339143399,1.6119890501849212,1.6119890501849212,-0.32364409356785062]
[97,5.6312473117793416E-2,-9.2755161747922674,-9.2755161747922674,-5.6869019066616291]
[98,0.80804733641082538,7.7494873745898598,7.7494873745898598,7.2033579630753266]
[99,0.49894266970018275,1.983082689986011,1.983082689986011,5.0292447211739599]
[100,0.32081795804802316,-1.0000613650770944,-1.0000613650770944,6.3504126906509022]

{"sheet":"LogNormal","index":17,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[12,4,12,6],[14,4,14,6],[0,0,0,4],[4,4,4,7],[9,4,9,6],[10,4,10,6],[11,4,11,6]]}
["UNIVARIATE LOGNORMAL"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"Lognormal($F$7,$F$8)","v":6.4061426370973651}]
[{"$f":"A4+1","v":2},1.4325626343406375,null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},2.9313694644032222,null,null,"Name","Value","Type","Feasible Range"]
[4,1.3877542266535385,null,null,"mu = ",1,"Location","Any finite real number"]
[5,1.4723380191628226,null,null,"sigma = ",0.5,"Scale","Real number greater than zero"]
[6,3.3458720636774832]
[7,4.139861782170752,null,null,"Distribution Type:",null,null,"Continuous"]
[8,3.0849194075143025,null,null,"Distrbution Name:",null,null,"Lognormal"]
[9,2.0394714565202654,null,null,"Variate Number:",null,null,"Univariate"]
[10,5.8437986825774546,null,null,"Simulation Method:",null,null,"Convolution"]
[11,4.1003217946372557]
[12,1.9730052745095359,null,null,"Macro Format:",null,null,"=Lognormal(mu, sigma)"]
[13,4.0732616797772412]
[14,1.5973434136564912]
[15,4.4150613893749266,null,null,null,null,"Notes:","1. The Lognormal distribution does not lend"]
[16,5.7937705462426319,null,null,null,null,null,"itself easily to a manual presentation so no"]
[17,2.1233296819909824,null,null,null,null,null,"manual example is provided here, only the"]
[18,2.5233121242281911,null,null,null,null,null,"output of the macro generated variates."]
[19,5.4835515423548218]
[20,2.5368189644159798]
[21,1.8023168948831663]
[22,1.2563107132316185]
[23,4.6587934072659491]
[24,1.8479814753319577]
[25,2.6596971587770746]
[26,3.3710320521813228]
[27,1.4107682416362499]
[28,2.2776313738068779]
[29,3.6781914961673525]
[30,3.0800279617039257]
[31,3.9451193543689782]
[32,2.2171582333009736]
[33,4.3333249034126986]
[34,2.9412305553170746]
[35,2.6538158748729952]
[36,4.347334783921089]
[37,1.7312668763798782]
[38,2.7308309139757525]
[39,2.9241421667571852]
[40,1.8561254774502802]
[41,4.3652684227358103]
[42,3.0608896263184042]
[43,3.9569140697856575]
[44,1.3860566038502071]
[45,7.1813058113331349]
[46,1.5992782770270522]
[47,3.538175849760504]
[48,2.430686150351856]
[49,2.3895413020361271]
[50,0.77234248353161961]
[51,3.3627885666186943]
[52,4.2183996586472725]
[53,2.2210462731660878]
[54,1.936017900827548]
[55,3.7535097276090017]
[56,2.9530297826783398]
[57,1.6723119167443392]
[58,3.2348914244395384]
[59,5.082492292637764]
[60,4.2674925849666936]
[61,4.8712572039336441]
[62,4.6005001929468659]
[63,2.9081391633266476]
[64,2.7992229560966213]
[65,3.7566197785651827]
[66,{"$f":"Lognormal($F$7,$F$8)","v":1.468356240803782}]
[{"$f":"A69+1","v":67},2.7576150233727463]
[68,1.8685383267262705]
[69,4.0563556596159751]
[70,1.5231160809887014]
[71,2.8962501020150193]
[72,9.4549204325029628]
[73,2.3873003314897012]
[74,3.6692244855160334]
[75,2.0511522700290041]
[76,2.6491113817579799]
[77,4.3424525987933711]
[78,1.9291547925669927]
[79,2.2418535729383424]
[80,1.8062647201050048]
[81,2.9219061406738902]
[82,6.0409529105243758]
[83,4.8646057723436344]
[84,3.3240408185989336]
[85,1.9940680136352551]
[86,1.3570031165812404]
[87,2.7364976011593765]
[88,1.7512778624411041]
[89,1.4333279364345257]
[90,3.4789642432461685]
[91,3.6075375111842218]
[92,4.0037043475779397]
[93,2.604214593922181]
[94,2.3254873682672335]
[95,1.4494053238509426]
[96,2.0652158035882571]
[97,1.5620084101547922]
[98,2.5237785721681356]
[99,0.52793113271620296]
[100,6.9065220981206261]

{"sheet":"Multinomial","index":18,"n_rows":118,"n_cols":24,"rows_kept":118,"cut":false,"hidden":false,"merged":[[21,10,21,12],[0,0,0,10],[5,10,5,13],[16,10,16,12],[17,10,17,12],[18,10,18,12],[19,10,19,12]]}
["MULTIVARIATE MULTINOMIAL"]
[]
[]
["Observation\nNumber","Macro\nGenerated\nEvent #1","Macro\nGenerated\nEvent #2","Macro\nGenerated\nEvent #3","Macro\nGenerated\nEvent #4","Macro\nGenerated\nEvent #5","Macro\nGenerated\nEvent #6","Total Across\nAll Events,\nper Observ."]
[1,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":18},21,30,9,14,8,{"$f":"SUM(B5:G5)","v":100}]
[{"$f":"A5+1","v":2},{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},24,24,10,19,6,{"$f":"SUM(B6:G6)","v":100},null,null,"Population Parameters"]
[{"$f":"A6+1","v":3},{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},15,31,24,9,7,100,null,null,"Name","Value","Type","Feasible Range"]
[{"$f":"A7+1","v":4},{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},21,24,22,15,2,100,null,null,"events =",6,"Shape","Any Finite Positive Integer"]
[5,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":19},22,28,14,12,5,100,null,null,"prob(1)",0.15,"Shape","A vector of probabilities in range [0,1] sum to 100%"]
[6,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},20,33,14,16,6,100,null,null,"prob(2)",0.2,"Shape","A vector of probabilities in range [0,1] sum to 100%"]
[7,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},19,33,19,11,6,100,null,null,"prob(3)",0.3,"Shape","A vector of probabilities in range [0,1] sum to 100%"]
[8,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},20,26,21,14,4,100,null,null,"prob(4)",0.16,"Shape","A vector of probabilities in range [0,1] sum to 100%"]
[9,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},17,27,17,12,12,100,null,null,"prob(5)",0.12,"Shape","A vector of probabilities in range [0,1] sum to 100%"]
[10,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},20,29,15,17,6,100,null,null,"prob(6)",7.0000000000000007E-2,"Shape","A vector of probabilities in range [0,1] sum to 100%"]
[11,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},20,37,12,7,8,100,null,null,"n = ",100,"Shape","Any Finite Positive Integer"]
[12,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},20,29,19,11,8,100]
[13,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":22},19,32,14,8,5,100,null,null,"Distribution Type:",null,null,"Discrete"]
[14,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},17,32,16,14,4,100,null,null,"Distrbution Name:",null,null,"Multinomial"]
[15,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":21},21,33,11,9,5,100,null,null,"Variate Number:",null,null,"Multivariate"]
[16,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},20,22,20,12,11,100,null,null,"Simulation Method:",null,null,"Convolution"]
[17,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":9},15,29,25,12,10,100]
[18,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},19,39,16,6,3,100,null,null,"Macro Format:",null,null,"=Multinomrv(events, prob,n)"]
[19,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},20,33,14,10,11,100]
[20,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":18},25,21,16,9,11,100,null,null,null,null,"Notes:","1. The Multinomial distribution does not lend"]
[21,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},25,26,18,9,8,100,null,null,null,null,null,"itself easily to a manual presentation so no"]
[22,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":10},16,34,16,16,8,100,null,null,null,null,null,"manual example is provided here, only the"]
[23,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},22,31,17,9,8,100,null,null,null,null,null,"output of the macro generated variates."]
[24,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},19,27,21,9,8,100,null,null,null,null,null,"2. For each simulation, the total events simulated"]
[25,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},18,31,16,10,10,100,null,null,null,null,null,"should equal n, the total number of runs"]
[26,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},19,34,13,12,9,100,null,null,null,null,null,"3. The total number of events must equal the total"]
[27,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},21,32,16,10,9,100,null,null,null,null,null,"number of individual event probabilities provided."]
[28,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},26,27,16,9,9,100,null,null,null,null,null,"4.  The sum of the event probabilities provied must"]
[29,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},16,27,13,19,8,100,null,null,null,null,null,"equal 100%."]
[30,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},18,32,9,20,6,100]
[31,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},30,29,14,12,4,100]
[32,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},16,32,12,15,9,100]
[33,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":19},20,26,18,9,8,100]
[34,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},26,31,15,7,5,100]
[35,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},25,23,20,10,5,100]
[{"$f":"A39+1","v":36},{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":19},23,17,16,19,6,100]
[37,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":20},19,30,15,9,7,100]
[38,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},17,35,13,15,7,100]
[39,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":24},23,23,13,13,4,100]
[40,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":8},20,38,16,14,4,100]
[41,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":20},20,25,16,12,7,100]
[42,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":19},13,32,15,12,9,100]
[43,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},19,29,18,12,6,100]
[44,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},21,30,11,13,10,100]
[45,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},22,35,12,12,5,100]
[46,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":10},10,47,18,8,7,100]
[47,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},27,22,13,15,8,100]
[48,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},20,21,19,18,7,100]
[49,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},20,40,15,7,7,100]
[50,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},15,35,18,8,7,100]
[51,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},24,26,16,14,8,100]
[52,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},18,30,17,12,8,100]
[53,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},22,33,16,7,9,100]
[54,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},15,37,14,12,9,100]
[55,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":18},19,29,17,9,8,100]
[56,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},14,28,21,17,7,100]
[57,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},23,32,10,16,7,100]
[58,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},20,33,12,14,8,100]
[59,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":10},22,28,24,11,5,100]
[60,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":10},18,33,24,14,1,100]
[61,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},18,35,12,13,8,100]
[62,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},16,35,16,13,9,100]
[63,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},23,27,14,14,10,100]
[64,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":10},22,36,11,16,5,100]
[65,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},21,26,15,14,11,100]
[66,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},15,29,15,18,7,{"$f":"SUM(B70:G70)","v":100}]
[{"$f":"A70+1","v":67},{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},19,31,19,10,6,100]
[68,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},32,23,17,10,4,100]
[69,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},19,35,13,11,10,100]
[70,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},22,32,16,13,4,100]
[71,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},19,33,23,7,6,100]
[72,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},26,30,13,8,7,100]
[73,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},24,24,11,11,14,100]
[74,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},27,26,15,17,3,100]
[75,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},25,30,20,7,6,100]
[76,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},21,33,14,12,5,100]
[77,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},26,25,14,13,5,100]
[78,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},24,29,15,14,6,100]
[79,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":18},16,34,16,7,9,100]
[80,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},18,38,14,14,5,100]
[81,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},26,30,17,12,1,100]
[82,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},15,30,22,6,10,100]
[83,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":23},17,31,15,5,9,100]
[84,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},15,28,17,17,9,100]
[85,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":18},16,25,15,20,6,100]
[86,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},23,28,23,7,5,100]
[87,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},14,39,16,11,9,100]
[88,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":17},15,37,15,13,3,100]
[89,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},19,28,21,10,9,100]
[90,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":15},18,30,22,12,3,100]
[91,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":20},20,34,15,8,3,100]
[92,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},22,34,12,14,7,100]
[93,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":21},19,27,17,14,2,100]
[94,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":16},19,24,16,15,10,100]
[95,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},22,27,20,15,2,100]
[96,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":6},18,33,13,13,17,100]
[97,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":13},23,34,15,6,9,100]
[98,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":14},22,34,14,9,7,100]
[99,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":11},19,31,20,12,7,100]
[100,{"$f":"Multinomrv($L$8,$L$9:$L$14,$L$15)","v":12},16,29,24,11,8,100]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF($Q118<B$3,1,0)","v":0},{"$f":"SUM(S18:S117)","v":0},0,0,0,0,{"$f":"SUM(X18:X117)","v":0}]

{"sheet":"Negative Binomial","index":19,"n_rows":103,"n_cols":16,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,12,14,14],[0,0,0,11],[4,12,4,15],[9,12,9,14],[10,12,10,14],[11,12,11,14],[12,12,12,14]]}
["UNIVARIATE NEGATIVE BINOMIAL"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate #1","Uniform\nRandom\nVariate #2","Uniform\nRandom\nVariate #3","Uniform\nRandom\nVariate #4","Uniform\nRandom\nVariate #5","Uniform\nRandom\nVariate #6","Uniform\nRandom\nVariate #7","Negative\nBinomial\nRandom \nVariate","Macro\nGenerated\nVariate, uniforms\nsubmitted","Macro\nGenerated\nVariate w/o\nUniforms\nsubmitted"]
[1,0.26868953420160424,0.44405580182317539,0.94465851721428806,0.49888612422971823,9.63488697880579E-2,9.3226344771026315E-2,0.11924615436169383,{"$f":"FLOOR(LN($B4)/LN($N$7),1)+FLOOR(LN($C4)/LN($N$7),1)+FLOOR(LN($D4)/LN($N$7),1)+FLOOR(LN($E4)/LN($N$7),1)+FLOOR(LN($F4)/LN($N$7),1)+FLOOR(LN($G4)/LN($N$7),1)+FLOOR(LN($H4)/LN($N$7),1)","v":40},{"$f":"NegBinomial($N$7,$N$8,$B4:$H4)","v":40},{"$f":"NegBinomial($N$7,$N$8)","v":23}]
[{"$f":"A4+1","v":2},0.79377423808874648,0.65718795300261768,8.3902096450906072E-2,0.59983503317384124,0.62426304440459734,0.91802688414454214,7.8087686772897458E-3,{"$f":"FLOOR(LN($B5)/LN($N$7),1)+FLOOR(LN($C5)/LN($N$7),1)+FLOOR(LN($D5)/LN($N$7),1)+FLOOR(LN($E5)/LN($N$7),1)+FLOOR(LN($F5)/LN($N$7),1)+FLOOR(LN($G5)/LN($N$7),1)+FLOOR(LN($H5)/LN($N$7),1)","v":38},38,{"$f":"NegBinomial($N$7,$N$8)","v":29},null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.22897348669921869,0.16854099652803767,0.7880284345439279,0.3099187159890805,0.85061759994125308,0.54577234848232525,21,21,43,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.59746096109928493,0.92699625340972147,3.3603836690073163E-2,0.92758929924540767,0.96118627038557669,0.14065506242060088,26,26,37,null,"prob = ",0.8,"Location","Any real number between 0 and 1, inclusive"]
[5,0.86717342695468203,0.12564729724809154,0.7808885858361172,0.67530632241603794,0.82805754970063883,0.87520177772951457,0.77070063697100721,12,12,15,null,"k = ",7,"Shape","Any Finite Positive Integer"]
[6,0.27994300504477809,0.57228225911488473,0.55048393023289444,0.36090719085120559,0.14655897310343047,0.92739325317684185,0.15667105230573231,29,29,17]
[7,0.93667220783619842,0.29739908159505091,0.74320952910312843,0.17084449145162306,3.7645333056332553E-2,5.1473729609779917E-2,0.55401585235608841,42,42,19,null,"Distribution Type:",null,null,"Discrete"]
[8,0.43191155671140469,0.33552329929780045,0.23504453274061154,0.1289192128482497,0.99573050623093051,0.83358509352086874,0.27806884965063705,27,27,34,null,"Distrbution Name:",null,null,"Negative Binomial"]
[9,0.96203701528155405,0.79162900118788981,0.82409639266813339,0.88072724597550311,0.1036601397265301,0.26307517222225496,0.97908841635751276,16,16,57,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,0.24822859655358209,9.4476181769571177E-2,0.43698633361489625,0.52802532605770924,0.23307076973984708,0.61743007445709308,37,37,11,null,"Simulation Method:",null,null,"Convolution"]
[11,0.20171971836271319,0.14050226564731538,0.82450719990321852,0.42148541765256109,3.0325489419976703E-3,0.33326318867756177,0.80116780518975594,47,47,26]
[12,0.58041618261550787,0.24325661202272519,0.2353386720939582,0.25639836713009945,0.81401486349769503,9.0828959308358992E-2,0.90758681691420595,30,30,18,null,"Macro Format:",null,null,"=Negbinomial(prob, k)"]
[13,0.34366851316718994,0.66165916832683569,0.41783635199453883,0.22118218038386972,0.20130163587259031,0.34950246160939791,0.64123518709550864,26,26,42]
[14,0.9651686825697714,0.56279612960791148,0.20895868808346618,0.46364262035621306,0.16972679136835811,0.14139170557370395,0.42552336256093326,30,30,45]
[15,0.38704808829902526,0.97513917603786493,0.61849323117375588,0.10286499850614572,0.48366925251296766,0.9016041161399484,0.72679878758129601,20,20,27]
[16,0.86385756571325945,0.43110523880919793,0.41341397746668018,0.1414194199651041,0.59472517243126566,0.76342508157800615,0.16572524205532524,25,25,26]
[17,0.17476282037902591,8.3728507126800911E-2,0.45125352252218764,0.53115031103021348,0.37398147849794616,0.66961267637596589,0.67493411525208225,29,29,37]
[18,0.38117659587117037,6.6163538436367908E-2,0.55095601736724475,0.24121868241910183,0.48619923140627641,0.55178239785731031,0.86008080692805722,29,29,31]
[19,0.87794506028866293,5.8800603133947305E-2,0.76916565784570079,0.63154489097232969,0.28914261401619501,2.3419862767994681E-2,0.55094621250377018,38,38,20]
[20,0.18238019015349183,0.91427131754721946,0.2074303217864526,0.34259128604568745,0.52824300608824704,0.57238047928552127,0.70237562982859036,23,23,11]
[21,0.39753335201985007,0.99208452571603889,0.98968210720256233,0.20615792323879945,0.30161026595052942,0.50035765055805559,1.0524162000349779E-2,39,39,35]
[22,0.74199757940000399,0.33932002996360344,0.29329530229659517,0.74672409361448933,0.57613284838298062,0.12278104423902592,0.67462563324256697,23,23,11]
[23,0.57082894586967958,0.51026222064659499,0.64378712951547401,0.82493185552957493,0.91463687911771674,0.5076080193625998,0.66360191230678578,10,10,25]
[24,0.90195869363590486,0.68823388521184869,0.26034861785763719,0.43932967596023664,0.85435089758864236,0.74690899636827601,0.17395545948528424,18,18,45]
[25,0.43843055863807978,0.3802352804098853,0.48875636874668416,0.98737245508274019,0.75550845086423768,0.35509000042603223,0.59480100668656222,17,17,26]
[26,0.3929492390413114,0.81007583244623871,0.90611446184834976,0.73028965436657967,0.52300617319269782,0.87176304416969497,0.63173178226649018,9,9,23]
[27,0.2515715048326993,7.1945023913193018E-2,0.50583283519150479,0.15100842200827502,3.6233927895830131E-2,0.38049179171909764,0.85016699205469193,46,46,31]
[28,0.30550021398012439,6.0405119249104633E-2,0.34033602191558809,0.42209073630234029,0.31133184998632724,0.23369818567419975,0.72962648456275914,36,36,18]
[29,7.9387447484473794E-2,0.36390303471752294,0.90607542650280681,0.75632244023626993,0.58036510544181064,0.69475809712404324,0.64068443059669566,20,20,19]
[30,0.82057811417206794,2.3405931264653845E-2,0.7012680027746645,0.14225638890191872,0.75917254336870554,0.93463302896457301,0.18541556001810533,33,33,20]
[31,5.0767455327721533E-3,0.72094892071410632,0.14077946580881839,0.82032331518940493,0.10776961308859778,0.12907395402798028,0.17053330229606589,57,57,19]
[32,2.9980457362279278E-2,0.50045935317620716,0.32217442373509508,0.47869096147227719,0.55807866226191816,0.14831379773373055,0.1611329949618141,44,44,24]
[33,0.89698739215075429,0.5185423769601476,0.41695106754313338,0.99239279451181472,5.968611419889347E-2,3.7519897421968373E-2,0.95365164737945263,31,31,30]
[34,4.8518018441997213E-2,0.73465611364814176,0.45990089231225773,0.5773846898612669,0.13439929113262827,0.43375313990839715,0.2312891310468026,36,36,27]
[35,0.37123916516677757,0.92262882703722793,0.60087959654199052,0.90528832704027873,0.47403175390697228,0.74613708590864314,0.51401655416016057,12,12,26]
[36,0.18273885825049341,0.70297388611730971,0.41743434261957091,5.3776221000129243E-2,0.92463657425874057,4.4938495817940738E-2,0.74884577543770892,38,38,29]
[37,0.12050005291704391,0.48699160733047131,0.79854695145178001,0.39489054994311357,4.3082671271250206E-2,5.1489985169852481E-3,0.66580405215093585,55,55,16]
[38,0.64945693361731327,0.11771898978083439,3.1453777220467383E-2,2.3782779554623046E-2,0.80366524333729239,0.67667373800564989,0.98267258301130289,42,42,39]
[39,0.84523354850406707,0.93147610649873314,0.7227030982250009,0.85963805879282773,0.43289966488460607,0.33526595300625361,0.68756227448055884,9,9,23]
[40,0.96559113278394504,0.52180085869870974,0.36085133601913555,0.12440347074229197,0.89358801039548452,0.30700203175416052,0.65238038775693818,21,21,21]
[41,0.66499232931154673,0.72501602030632817,0.38693248732470809,2.2260548661534929E-2,1.6525030432561372E-2,0.89518862995787418,0.88185734416296357,41,41,36]
[42,0.48716817186481609,0.50203712162708591,0.61023482778033322,0.13104379579847802,0.94876941793097813,7.7893617773898138E-2,0.40175400334604028,32,32,37]
[43,0.77210315614728597,0.45847626516131068,0.58003721433938082,0.44415130341552289,0.84265241818595837,0.76447272294425284,0.46249900968999003,13,13,25]
[44,0.82636627627465631,0.2765273183663941,5.9388649347640765E-2,0.41267253660556658,0.94500924785849738,0.1629516516408539,0.35068718722389947,32,32,14]
[45,0.30996283637913491,0.15196584628760113,0.92957314107007982,0.79261822755734368,0.90906594417631015,0.86652546747056636,6.9907098986668914E-2,25,25,32]
[46,0.1840653161997976,0.40443685419245889,0.87408911659487432,0.25180653470572434,9.4276343175194621E-2,0.15668580202679661,0.1368271528970133,43,43,11]
[47,0.58275788798882977,0.51568403043388444,0.44301428650688701,0.2451710697180467,0.39833740174041821,1.3944395329431925E-2,0.55781898761101589,38,38,56]
[48,0.3211056530871087,0.88707475191810981,9.2598313034766844E-2,0.2891176650001267,0.50001696445442201,0.57007562577295368,0.88420600791876236,25,25,32]
[49,0.94059973373021577,0.12199706419429013,0.57705540086425366,0.81808384594513595,4.5318035527652345E-2,0.94711126032404858,0.89140581044253508,24,24,13]
[50,0.14907620621989892,0.5485823647611463,0.26796530810244401,0.21952720594787811,0.36154336839763968,0.31777841576637189,0.22763980918811466,36,36,16]
[51,0.38302044178353878,0.54107979941368844,0.18711104130384804,0.36722038571383531,0.59813420561627439,0.9892828019299893,0.24495161099784046,25,25,19]
[52,8.4815952479745493E-2,1.6353855701170983E-2,0.43364037164232572,0.23540635657850706,0.12507276441986082,0.3447163615124974,0.38457562033908521,55,55,25]
[53,0.84221407414122895,0.4652930510870229,0.23495666686238392,7.1608469861346613E-2,0.84496171990889513,0.62492740094331245,0.92529320470534515,22,22,58]
[54,0.40498559499715014,0.64175961031266415,0.17319708286410218,0.99569633649613354,7.3232864520601515E-3,1.2808531333711293E-2,0.39454366109127237,57,57,41]
[55,0.31192254229901473,0.384294644489242,0.49906889542757915,0.58155200720445932,0.22075959401793743,0.67644331763222698,0.46032556339866315,24,24,30]
[56,7.3945219604894419E-2,0.26715954448559143,0.53594573165479953,0.14378757291087185,0.78509729565243125,0.58076291586251172,0.73713309747665212,30,30,43]
[57,0.41540561914582874,0.43564406875484152,0.76465240175288818,0.73597608744136589,0.44092761059884067,0.89141421781484664,9.5760459546443855E-2,21,21,54]
[58,0.94334481547755944,0.64841364201228391,0.10106244218475435,0.37465241097256619,0.15885608636138859,0.28879635201970133,0.50521758873022016,31,31,14]
[59,0.6294690698059815,0.31342593702642774,0.27999663957185783,0.797712258076687,0.97554420231398031,0.1778556759072395,0.9554329436906237,20,20,41]
[60,0.21751765244325438,8.4241915546240942E-2,7.6231579349971379E-2,0.77883884135572168,4.2973587007961389E-2,0.46526317958107355,0.39204334912332972,50,50,26]
[61,0.81132182231923589,0.68530048572932756,0.91843321793348964,0.87078609678800201,0.45717511120216625,0.76702017936304512,0.12070228102247393,14,14,38]
[62,0.47641953418452843,0.49373831416690117,0.61116889863213786,0.13677772832920221,0.983538823626248,0.6915807454954539,0.96054304312971439,17,17,23]
[63,0.92308615531225435,0.82856125921562329,0.67135354273510084,0.38706028641485202,0.94162374400265936,0.87575791579838369,0.47862942255948415,8,8,30]
[64,0.62241658364570296,0.99521523300006831,0.15108467654332614,0.13182799022577973,0.20076209511189935,7.6786451973095415E-3,0.91073778351494639,47,47,18]
[65,0.56290274788396399,0.57439239559870603,0.94001077530971422,0.79083059029753733,0.12868770780541583,0.49658633995084855,0.97282140880468793,17,17,18]
[66,0.27617460253729631,0.90514549193163008,0.93238631014475204,0.72004724911869522,1.5207213473711012E-2,0.14124940681356268,0.97409958752198067,{"$f":"FLOOR(LN($B69)/LN($N$7),1)+FLOOR(LN($C69)/LN($N$7),1)+FLOOR(LN($D69)/LN($N$7),1)+FLOOR(LN($E69)/LN($N$7),1)+FLOOR(LN($F69)/LN($N$7),1)+FLOOR(LN($G69)/LN($N$7),1)+FLOOR(LN($H69)/LN($N$7),1)","v":32},{"$f":"NegBinomial($N$7,$N$8,$B69:$H69)","v":32},{"$f":"NegBinomial($N$7,$N$8)","v":14}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.42663573398542542,0.40268599968699748,0.46648308886850365,7.8097896811085921E-2,0.15469216615354309,0.10406671101240361,39,39,11]
[68,0.17855864253016906,0.92182682930756443,0.27487450479688469,0.59998569913931388,0.20239921292835883,0.45741513207029505,0.29431277079409401,29,29,49]
[69,0.14106716857892998,0.41316596081555601,0.22786742823371819,0.67549286065820424,0.60628011623117506,0.7188258255753831,0.50860538327200566,24,24,9]
[70,0.78799892820694739,0.10465423467224733,0.74837210120785669,0.79841454852660287,7.8566064599190577E-2,0.1515141803650254,0.80966139436599005,32,32,19]
[71,0.62019869479720879,3.7197902037881203E-2,0.19416544327049856,0.12837160179383356,0.76430208946843625,0.4974618589726667,0.72600342230786075,37,37,20]
[72,0.32070616340267466,0.34771751832010722,0.45035525860180958,0.64637311454866697,9.6923054175458656E-2,0.59979783204462722,0.87301022364969127,25,25,36]
[73,0.71916827005391148,0.62919972857465234,0.11435596958412531,0.43942490070084406,0.9878691149045844,0.18127906494341761,6.3812019019040989E-2,34,34,27]
[74,0.70290736382840724,0.33028691321614589,0.60341658426690092,0.98828558083875662,0.48942774820349144,3.5778795498131899E-2,1.3143018336182033E-2,43,43,19]
[75,0.154172834186179,0.82934810072780096,0.97519129510717062,0.66863378854350475,0.57432083636357789,0.19329622125990009,0.64505361838847464,19,19,23]
[76,0.27977295388613965,0.2479116645837256,0.90015875266033063,0.82798540785461017,0.75042584489901865,0.46445682008699596,0.78554631005836639,16,16,24]
[77,0.42321062277449939,0.11691194355116818,0.18268005882632721,0.57863070299224251,0.65154362177907565,0.81331363482318131,0.34602150169604473,26,26,29]
[78,0.98136142771892321,0.2126052668686973,0.49378432861767929,0.12917870966829981,0.17037939374521316,0.17639705247165427,0.61437131575961945,34,34,48]
[79,0.20085756040090119,0.54482783306965632,0.15206980415878835,0.80649843587074299,0.46794337762397409,9.9669387719940383E-2,8.7422034934123372E-2,40,40,36]
[80,0.16133779816984994,4.8198744566575136E-2,0.83830783611343196,0.18046025675183097,0.71784600312470304,0.72332414312747417,0.96761793291909071,30,30,19]
[81,0.25863578352871763,0.42254787054736553,0.77893307474131113,0.14905719793036742,0.48267683924500737,0.36737654554779875,0.12522263003024947,34,34,23]
[82,0.8347220398143228,0.39308391964321521,0.34844397558988538,0.68209905343015476,3.1969902411721485E-4,0.14905460173087837,4.836536615533038E-2,66,66,18]
[83,0.51591167107959424,0.85182300536064515,0.29184570629979889,0.19791537152532712,8.343290608135856E-2,0.62569509198140727,0.18028680782988771,34,34,28]
[84,0.24633192212221666,0.11812905311926203,0.8600294725604537,0.50617864033560112,0.9207569090563027,0.26636195462233647,0.7092825074676069,24,24,11]
[85,0.59063871388364364,0.42056439810769575,0.80770427139800016,0.83277849811506122,0.17082366589778664,0.95643767012414227,0.49649529007552617,15,15,33]
[86,0.65393134749071002,1.4831636671858162E-2,0.31721254355102813,0.25331650531851324,0.35754387192920722,8.8694904205437131E-2,0.5125265437487655,46,46,34]
[87,0.56445460206933995,0.36716035465117058,0.14728906509629813,2.7228034984578153E-2,0.89765836586751635,0.41335975025087734,0.58564927042993487,35,35,18]
[88,0.10565266639072934,0.2451461442845756,0.75699264474447314,0.18836523515263148,0.38905069115978863,0.91493203869986917,0.42026023075945995,31,31,34]
[89,0.59226465879030998,0.20324185152060736,0.5569816922545987,0.82250809269997516,0.4961883902071127,0.35918682100226806,0.8565024038320761,18,18,39]
[90,0.72089126375496948,0.6153593343442274,0.34490514828723084,0.64566155333166775,0.58820323178895351,0.28168345267729633,0.71170462173921156,16,16,17]
[91,0.58803803186325454,0.23156698246912066,0.20833596652013231,5.9584644967523137E-2,0.25220618830623598,0.14212910625429498,0.85035345434684617,41,41,21]
[92,0.76602838211191659,0.24775133853500109,0.74177770730494508,0.34224498107278167,0.71429842526070986,0.20540188219524902,0.61207450207107217,22,22,35]
[93,0.48285856602942256,1.9371888135073734E-2,0.59734241484469186,8.8849935776666777E-2,0.76119032606566261,0.39076942525454483,0.59894725982057995,39,39,36]
[94,0.62864718503333628,0.85525903591075469,0.72651082792566446,0.17568537894663494,0.65898770931263762,0.79790489759395022,0.72742497020319064,13,13,9]
[95,0.33779794281158637,0.96600502897790752,0.72890849591978657,0.1676091166598157,0.10220556688681359,4.4334465319983418E-2,0.11393338647820017,45,45,29]
[96,0.47576831339143399,0.12342088429061493,0.84500439278961514,0.37133314322368338,0.22985233234476043,0.53774209685275065,0.64227973468394028,25,25,36]
[97,5.6312473117793416E-2,0.82615584090670624,0.39746820194220911,0.76770033709774821,0.78833912500599979,0.46660878586295595,0.86543242380584318,21,21,22]
[98,0.80804733641082538,0.26781166835787318,0.15190694068306676,0.60802719908661262,0.42566726357463358,0.99783316657343102,0.75968364381620757,19,19,12]
[99,0.49894266970018275,0.59543950981597049,0.48996129064447658,0.18064518783684902,0.67372558960368534,0.7458464568176949,0.79585881430679739,18,18,30]
[100,0.32081795804802316,0.15219174065625574,0.12761995369866286,0.72357288320741242,0.46971588822023025,2.6892131528586716E-2,0.82342354055942402,42,42,25]

{"sheet":"Normal (B-M)","index":20,"n_rows":103,"n_cols":11,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,7,14,9],[0,0,0,5],[9,7,9,9],[10,7,10,9],[11,7,11,9],[12,7,12,9],[4,7,4,10]]}
["UNIVARIATE NORMAL (BOX-MULLER)"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate #1","Uniform\nRandom\nVariate #2","Normal\nRandom\nVariate #1","Macro\nGenerated\nVariate, uniforms\nsubmitted","Macro\nGenerated\nVariate w/o\nUniforms\nsubmitted"]
[1,0.26868953420160424,0.44405580182317539,{"$f":"$I$8*SQRT(-2*LN($B4))*COS(2*PI()*$C4)+$I$7","v":-1.0442048090075433},{"$f":"Normal_bm($I$7,$I$8,$B4:$C4)","v":-1.0442048090075433},{"$f":"Normal_bm($I$7,$I$8)","v":0.51012346791175123}]
[{"$f":"A4+1","v":2},0.79377423808874648,0.65718795300261768,1.2514967095067755,1.2514967095067755,0.44318426344289974,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.22897348669921869,2.1649677424747842,2.1649677424747842,2.5031659051645727,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.59746096109928493,0.52222500760856083,0.52222500760856083,1.7224767374751775,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,0.12564729724809154,2.7519496024205798,2.7519496024205798,9.4060599763388097E-3,null,"sigma =",2,"Scale","Real number greater than zero"]
[6,0.27994300504477809,0.57228225911488473,-0.86792843147645993,-0.86792843147645993,2.2981309653531206]
[7,0.93667220783619842,0.29739908159505091,1.7877159927283162,1.7877159927283162,1.3554221540591289,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,0.33552329929780045,0.67345226258693169,0.67345226258693169,3.0341203626562407,null,"Distrbution Name:",null,null,"Normal"]
[9,0.96203701528155405,0.79162900118788981,2.1438885182423157,2.1438885182423157,0.29126275976405913,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,0.24822859655358209,2.043949037624742,2.043949037624742,4.1262867103470393,null,"Simulation Method:",null,null,"Box-Muller Transform Method"]
[11,0.20171971836271319,0.14050226564731538,4.2724283470831583,4.2724283470831583,3.4665433357659552]
[12,0.58041618261550787,0.24325661202272519,2.0883642207062314,2.0883642207062314,-0.24926619509910664,null,"Macro Format:",null,null,"=Normal_BM(mu, sigma, [unif])"]
[13,0.34366851316718994,0.66165916832683569,0.45952872865583605,0.45952872865583605,1.3427786902888021]
[14,0.9651686825697714,0.56279612960791148,1.5083596487060924,1.5083596487060924,-2.9231436773298949]
[15,0.38704808829902526,0.97513917603786493,4.7221071421028284,4.7221071421028284,1.4495539258808618,null,null,null,"Notes:","1. Supplying uniform random variates to this"]
[16,0.86385756571325945,0.43110523880919793,1.0177784321097723,1.0177784321097723,4.5934711608276704,null,null,null,null,"macro is optional but if supplied there must be"]
[17,0.17476282037902591,8.3728507126800911E-2,5.2304649464216437,5.2304649464216437,-0.5526163374115014,null,null,null,null,"TWO uniform variates provided for each"]
[18,0.38117659587117037,6.6163538436367908E-2,4.5411672338263909,4.5411672338263909,0.96867817711594784,null,null,null,null,"normal RV generated by the macro."]
[19,0.87794506028866293,5.8800603133947305E-2,2.9516180848185818,2.9516180848185818,2.5005940508544384,null,null,null,null,"2. While the Box-Muller method is designed to"]
[20,0.18238019015349183,0.91427131754721946,5.1671784995464574,5.1671784995464574,0.53812509208637316,null,null,null,null,"return two normal variates, the macro returns"]
[21,0.39753335201985007,0.99208452571603889,4.713221804715956,4.713221804715956,2.0804322012236169,null,null,null,null,"only one.  In this case the normal variate from"]
[22,0.74199757940000399,0.33932002996360344,1.1776854476482224,1.1776854476482224,3.807847635154662,null,null,null,null,"the \"sine\" version of the method is returned."]
[23,0.57082894586967958,0.51026222064659499,-0.1134576222150141,-0.1134576222150141,2.6749399786792702]
[24,0.90195869363590486,0.68823388521184869,1.6561810875027962,1.6561810875027962,-0.59441359258336002]
[25,0.43843055863807978,0.3802352804098853,0.12515509174955719,0.12515509174955719,-0.2935276635785935]
[26,0.3929492390413114,0.81007583244623871,3.007518180256497,3.007518180256497,-0.97179975927020967]
[27,0.2515715048326993,7.1945023913193018E-2,4.9889403007652726,4.9889403007652726,2.077271391293305]
[28,0.30550021398012439,6.0405119249104633E-2,4.8608220131435491,4.8608220131435491,1.671356665843976]
[29,7.9387447484473794E-2,0.36390303471752294,-0.95382989268409357,-0.95382989268409357,0.77507259913951576]
[30,0.82057811417206794,2.3405931264653845E-2,3.2441868236265754,3.2441868236265754,1.3828256534083616]
[31,5.0767455327721533E-3,0.72094892071410632,0.81990607154376405,0.81990607154376405,2.6751974631785012]
[32,2.9980457362279278E-2,0.50045935317620716,-3.2969276493602475,-3.2969276493602475,1.7106582104753074]
[33,0.89698739215075429,0.5185423769601476,{"$f":"$I$8*SQRT(-2*LN($B36))*COS(2*PI()*$C36)+$I$7","v":1.0737407748148318},1.0737407748148318,6.5879554197402639]
[34,4.8518018441997213E-2,0.73465611364814176,1.5264031465173213,1.5264031465173213,3.3655068249273712]
[35,0.37123916516677757,0.92262882703722793,4.489343827431207,4.489343827431207,-1.3454578130190211]
[36,0.18273885825049341,0.70297388611730971,0.92622842259485827,0.92622842259485827,-1.4515184457126598]
[37,0.12050005291704391,0.48699160733047131,-2.1007316051268683,-2.1007316051268683,3.264471995827817]
[38,0.64945693361731327,0.11771898978083439,3.3726689467159825,3.3726689467159825,4.1860656303416182]
[39,0.84523354850406707,0.93147610649873314,3.0539541400024333,3.0539541400024333,3.7687386029985794]
[40,0.96559113278394504,0.52180085869870974,1.4756954963368063,1.4756954963368063,6.119887096073958]
[41,0.66499232931154673,0.72501602030632817,1.7175636095705049,1.7175636095705049,4.5043624166060958]
[42,0.48716817186481609,0.50203712162708591,-0.39837958981716781,-0.39837958981716781,2.0506431191158336]
[43,0.77210315614728597,0.45847626516131068,0.61024413544738465,0.61024413544738465,-0.48982885665297893]
[44,0.82636627627465631,0.2765273183663941,1.7950724283726536,1.7950724283726536,1.6795433177429768]
[45,0.30996283637913491,0.15196584628760113,3.7685524807341966,3.7685524807341966,1.6938941192269839]
[46,0.1840653161997976,0.40443685419245889,-1.0360177086984117,-1.0360177086984117,2.3507640107634016]
[47,0.58275788798882977,0.51568403043388444,-6.8345240991159351E-2,-6.8345240991159351E-2,5.8628674870504982]
[48,0.3211056530871087,0.88707475191810981,4.2870889913251711,4.2870889913251711,1.8119260239033061]
[49,0.94059973373021577,0.12199706419429013,2.5041742008565069,2.5041742008565069,1.0721229198087232]
[50,0.14907620621989892,0.5485823647611463,-1.7217103981365671,-1.7217103981365671,2.3125368547590677]
[51,0.38302044178353878,0.54107979941368844,-0.67901391411759882,-0.67901391411759882,2.6655946080332833]
[52,8.4815952479745493E-2,1.6353855701170983E-2,6.4193326489918316,6.4193326489918316,2.587142612647384]
[53,0.84221407414122895,0.4652930510870229,0.85567993107621887,0.85567993107621887,5.561307258124085]
[54,0.40498559499715014,0.64175961031266415,0.30891858464605182,0.30891858464605182,2.9903675578817088]
[55,0.31192254229901473,0.384294644489242,-0.28102011465089705,-0.28102011465089705,-2.9539139331959925]
[56,7.3945219604894419E-2,0.26715954448559143,1.5088147768146376,1.5088147768146376,0.73798112127161786]
[57,0.41540561914582874,0.43564406875484152,-0.43724249652728586,-0.43724249652728586,3.2561022344782673]
[58,0.94334481547755944,0.64841364201228391,1.5930122949518024,1.5930122949518024,5.0646600645224282]
[59,0.6294690698059815,0.31342593702642774,1.2532618411458913,1.2532618411458913,0.97157837230115729]
[60,0.21751765244325438,8.4241915546240942E-2,5.0153472432457225,5.0153472432457225,0.51801741187067041]
[61,0.81132182231923589,0.68530048572932756,1.488595355081872,1.488595355081872,1.4197232368045638]
[62,0.47641953418452843,0.49373831416690117,-0.43361349741866029,-0.43361349741866029,0.93841426088492708]
[63,0.92308615531225435,0.82856125921562329,2.379127390960023,2.379127390960023,1.6765454791712353]
[64,0.62241658364570296,0.99521523300006831,3.9467249403496805,3.9467249403496805,4.762652232364383]
[65,0.56290274788396399,0.57439239559870603,{"$f":"$I$8*SQRT(-2*LN($B68))*COS(2*PI()*$C68)+$I$7","v":8.5886028630936195E-2},8.5886028630936195E-2,-0.44990908608498437]
[66,0.27617460253729631,0.90514549193163008,4.6552457363811524,{"$f":"Normal_bm($I$7,$I$8,$B69:$C69)","v":4.6552457363811524},{"$f":"Normal_bm($I$7,$I$8)","v":1.2541076977297243}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.42663573398542542,1.6569756909814779,1.6569756909814779,-2.9341602781268286]
[68,0.17855864253016906,0.92182682930756443,5.2736087239656984,5.2736087239656984,3.4502074571607704]
[69,0.14106716857892998,0.41316596081555601,-1.3836316271375577,-1.3836316271375577,0.43850251784216532]
[70,0.78799892820694739,0.10465423467224733,3.092727215155902,3.092727215155902,3.4470609604837561]
[71,0.62019869479720879,3.7197902037881203E-2,3.9017709163377141,3.9017709163377141,0.68777726907847114]
[72,0.32070616340267466,0.34771751832010722,0.26226212698627083,0.26226212698627083,1.3871056306325362]
[73,0.71916827005391148,0.62919972857465234,0.882377390565108,0.882377390565108,3.485101130090845]
[74,0.70290736382840724,0.33028691321614589,1.1883117545067774,1.1883117545067774,-2.4031715070395325]
[75,0.154172834186179,0.82934810072780096,3.8492782222577535,3.8492782222577535,3.9885249013988902]
[76,0.27977295388613965,0.2479116645837256,2.0418850786201137,2.0418850786201137,2.1850037056566807]
[77,0.42321062277449939,0.11691194355116818,3.9464136349859373,3.9464136349859373,6.4759160229151362]
[78,0.98136142771892321,0.2126052668686973,2.090318746592688,2.090318746592688,2.95787812836382]
[79,0.20085756040090119,0.54482783306965632,-1.4422653682727002,-1.4422653682727002,2.2535086507085968]
[80,0.16133779816984994,4.8198744566575136E-2,5.6463676354529007,5.6463676354529007,0.87299158898368656]
[81,0.25863578352871763,0.42254787054736553,-0.90732307300604687,-0.90732307300604687,2.0507670447752604]
[82,0.8347220398143228,0.39308391964321521,1.0590258146907443,1.0590258146907443,4.9256455086972668]
[83,0.51591167107959424,0.85182300536064515,3.3737217487083582,3.3737217487083582,-0.45503121205589592]
[84,0.24633192212221666,0.11812905311926203,4.4673045883935645,4.4673045883935645,1.3145762949779591]
[85,0.59063871388364364,0.42056439810769575,0.19796025347588153,0.19796025347588153,0.806070274732406]
[86,0.65393134749071002,1.4831636671858162E-2,3.8353743251457293,3.8353743251457293,4.2717064571375918]
[87,0.56445460206933995,0.36716035465117058,0.56383060214102554,0.56383060214102554,1.6430060712127332]
[88,0.10565266639072934,0.2451461442845756,2.1293015544484475,2.1293015544484475,1.0618248357699982]
[89,0.59226465879030998,0.20324185152060736,2.5927888455714441,2.5927888455714441,4.0162131848393985]
[90,0.72089126375496948,0.6153593343442274,0.78869021381711524,0.78869021381711524,1.4275798062255116]
[91,0.58803803186325454,0.23156698246912066,2.2381674105414886,2.2381674105414886,1.9866541097811525]
[92,0.76602838211191659,0.24775133853500109,2.0206306292729321,2.0206306292729321,1.1170848039146177]
[93,0.48285856602942256,1.9371888135073734E-2,4.3954937954116744,4.3954937954116744,3.4742902447797577]
[94,0.62864718503333628,0.85525903591075469,3.1835726961122259,3.1835726961122259,4.3653196801043057]
[95,0.33779794281158637,0.96600502897790752,4.8796392107110318,4.8796392107110318,2.3363558875955768]
[96,0.47576831339143399,0.12342088429061493,3.740762745639123,3.740762745639123,3.0420781004870143]
[97,5.6312473117793416E-2,0.82615584090670624,4.2089434110955812,4.2089434110955812,2.7106853400500412]
[98,0.80804733641082538,0.26781166835787318,1.8541691089922012,1.8541691089922012,0.12120091695563673]
[99,0.49894266970018275,0.59543950981597049,5.3070462388489892E-2,5.3070462388489892E-2,2.4938497450004027]
[100,0.32081795804802316,0.15219174065625574,3.7388766906652284,3.7388766906652284,-3.5035662514296035]

{"sheet":"Normal (Polar)","index":21,"n_rows":103,"n_cols":14,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,10,14,12],[0,0,0,9],[4,10,4,13],[9,10,9,12],[10,10,10,12],[11,10,11,12],[12,10,12,12]]}
["UNIVARIATE NORMAL (MARSAGLIA POLAR)"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate #1","Uniform\nRandom\nVariate #2","Uniform\nRandom\nVariate #1","Uniform\nRandom\nVariate #2","Sum of\nSquared\nUniforms","Normal\nRandom\nVariate #1","Normal\nRandom\nVariate #2","Macro\nGenerated\nVariate"]
[1,0.26868953420160424,0.44405580182317539,{"$f":"-1+2*B4","v":-0.46262093159679152},{"$f":"-1+2*C4","v":-0.11188839635364922},{"$f":"D4^2+E4^2","v":0.22653713959007457},{"$f":"IF(OR($F4>1,$F4<0.0000000000001),NA(),$D4*SQRT(-2*LN($F4)/$F4))*$L$8+$L$7","v":-1.3499731617508415},{"$f":"IF(OR($F4>1,$F4<0.0000000000001),NA(),$E4*SQRT(-2*LN($F4)/$F4))*$L$8+$L$7","v":1.1897834721781422},{"$f":"Normal_Polar($L$7,$L$8)","v":1.5683594564918737}]
[{"$f":"A4+1","v":2},0.79377423808874648,0.65718795300261768,{"$f":"-1+2*B5","v":0.58754847617749295},{"$f":"-1+2*C5","v":0.31437590600523535},0.44404542213510656,{"$f":"IF(OR($F5>1,$F5<0.0000000000001),NA(),$D5*SQRT(-2*LN($F5)/$F5))*$L$8+$L$7","v":4.2470209652068869},{"$f":"IF(OR($F5>1,$F5<0.0000000000001),NA(),$E5*SQRT(-2*LN($F5)/$F5))*$L$8+$L$7","v":3.2022995214717804},2.2204500743570543,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.22897348669921869,0.64396070338576128,-0.54205302660156263,0.70850687115299882,3.2702439671119494,0.93077390704857677,3.7002258122427518,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.59746096109928493,0.33039344722464525,0.19492192219856985,0.14715438572256978,5.3722402211403999,3.9895175026673009,4.5372748760386212,null,"mu = ",2,"Location","Any finite real number"]
[5,0.86717342695468203,0.12564729724809154,0.73434685390936405,-0.74870540550381692,1.0998250860772156,{"$error":"#N/A"},{"$error":"#N/A"},-0.96026424688944489,null,"sigma =",2,"Scale","Real number greater than zero"]
[6,0.27994300504477809,0.57228225911488473,-0.44011398991044381,0.14456451822976946,0.2145992240458956,-1.3335963653625695,3.0949884883895953,1.081213273235583]
[7,0.93667220783619842,0.29739908159505091,0.87334441567239685,-0.40520183680989819,0.92691899694027569,2.706804569339718,1.6720669364541805,2.1840653365820999,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,0.33552329929780045,-0.13617688657719063,-0.3289534014043991,0.12675448473338075,0.4451816094167711,-1.7558708456632885,0.87242898564994542,null,"Distrbution Name:",null,null,"Normal"]
[9,0.96203701528155405,0.79162900118788981,0.92407403056310811,0.58325800237577963,1.194102711296533,{"$error":"#N/A"},{"$error":"#N/A"},2.245125010229696,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,0.24822859655358209,-0.71519290848132977,-0.50354280689283581,0.76505625471549943,0.80317242089827556,1.1573547340851853,6.2857779130678475,null,"Simulation Method:",null,null,"Marsaglia Polar Method"]
[11,0.20171971836271319,0.14050226564731538,-0.59656056327457363,-0.71899546870536923,0.87283898967333018,1.3339473163514506,1.1972502190998102,2.5433871005400071]
[12,0.58041618261550787,0.24325661202272519,0.16083236523101574,-0.51348677595454961,0.28953571878600065,2.9412100063749529,-1.0049852899659637,3.957958565328207,null,"Macro Format:",null,null,"=Normal_Polar(mu, sigma)"]
[13,0.34366851316718994,0.66165916832683569,-0.31266297366562013,0.32331833665367138,0.20229288191792505,-0.48556311737811386,4.5702695888060365,0.71944216033871133]
[14,0.9651686825697714,0.56279612960791148,0.93033736513954279,0.12559225921582295,0.88130102854972148,2.9963714870326621,2.1345066325008797,3.8017701654000535]
[15,0.38704808829902526,0.97513917603786493,-0.22590382340194948,0.95027835207572986,0.9540614838513839,1.8581416923450602,2.5967357116693437,-5.9532761351615893E-2,null,null,null,"Notes:","1. The macro for the Polar Method differs from"]
[16,0.86385756571325945,0.43110523880919793,0.72771513142651889,-0.13778952238160413,0.5485552649852663,4.153480120220121,1.5922484164349522,2.3380785008709024,null,null,null,null,"the macro for the BM method insofar as the"]
[17,0.17476282037902591,8.3728507126800911E-2,-0.65047435924194819,-0.83254298574639818,1.1162447151467503,{"$error":"#N/A"},{"$error":"#N/A"},6.6904293369775241,null,null,null,null,"Polar Method does not require the user to"]
[18,0.38117659587117037,6.6163538436367908E-2,-0.23764680825765927,-0.86767292312726418,0.80933230700326397,1.6563505722716914,0.74530061786166235,1.510439325219699,null,null,null,null,"provide uniform random numbers as input."]
[19,0.87794506028866293,5.8800603133947305E-2,0.75589012057732585,-0.88239879373210539,1.3499975055662787,{"$error":"#N/A"},{"$error":"#N/A"},3.2285730639131636,null,null,null,null,"As a result, the \"Macro Generated Variate\""]
[20,0.18238019015349183,0.91427131754721946,-0.63523961969301634,0.82854263509443893,1.0900122725969645,{"$error":"#N/A"},{"$error":"#N/A"},1.3379926597626226,null,null,null,null,"column will not match either of the two columns"]
[21,0.39753335201985007,0.99208452571603889,-0.20493329596029985,0.98416905143207778,1.0105863775898676,{"$error":"#N/A"},{"$error":"#N/A"},-0.62067480784351536,null,null,null,null,"labeled \"Normal Random Variates.\"  This is to"]
[22,0.74199757940000399,0.33932002996360344,0.48399515880000799,-0.32135994007279312,0.33752352482543413,4.4556864067570174,0.36948940053531265,3.5408957773259662,null,null,null,null,"avoid the macro generating occasional #NA"]
[23,0.57082894586967958,0.51026222064659499,0.14165789173935917,2.0524441293189977E-2,2.0488210982437603E-2,7.5193966570714821,2.7996909404124466,3.4641487017132668,null,null,null,null,"values, as the manual approach does in this"]
[24,0.90195869363590486,0.68823388521184869,0.80391738727180972,0.37646777042369739,0.78801114772572256,3.2502600314111163,2.5854862874312534,3.1154837992034983,null,null,null,null,"spreadsheet."]
[25,0.43843055863807978,0.3802352804098853,-0.12313888272384044,-0.2395294391802294,7.253753667247094E-2,-9.4651810714700968E-2,-2.07451133549392,4.653688920467606]
[26,0.3929492390413114,0.81007583244623871,-0.21410152191737719,0.62015166489247742,0.43042754915624876,1.1525337903970185,4.4547120268870462,1.9588912946675403]
[27,0.2515715048326993,7.1945023913193018E-2,-0.4968569903346014,-0.85610995217361396,0.97979111905506577,1.7971413012464681,1.6504641088556837,1.1834593597510907]
[28,0.30550021398012439,6.0405119249104633E-2,-0.38899957203975122,-0.87918976150179073,0.92429530377668523,1.6788991925469192,1.274270301012419,0.8158304310469342]
[29,7.9387447484473794E-2,0.36390303471752294,-0.84122510503105241,-0.27219393056495411,0.78174921317090429,0.66467711357827119,1.5679316001689543,1.4553343604710085]
[30,0.82057811417206794,2.3405931264653845E-2,0.64115622834413588,-0.95318813747069231,1.319648934559325,{"$error":"#N/A"},{"$error":"#N/A"},1.9386709690297523]
[31,5.0767455327721533E-3,0.72094892071410632,-0.98984650893445569,0.44189784142821265,1.1750698135086433,{"$error":"#N/A"},{"$error":"#N/A"},-0.39382696398771211]
[32,2.9980457362279278E-2,0.50045935317620716,-0.94003908527544144,9.1870635241431131E-4,0.88367432586685057,1.00534799750077,2.0009720799139643,-0.46224571163069372]
[33,0.89698739215075429,0.5185423769601476,0.79397478430150858,3.7084753920295199E-2,0.63177123707995597,3.9146346723651391,2.0894282250215177,0.36591068178680697]
[34,4.8518018441997213E-2,0.73465611364814176,-0.90296396311600557,0.46931222729628352,1.0355978853759615,{"$error":"#N/A"},{"$error":"#N/A"},1.2720733189656561]
[35,0.37123916516677757,0.92262882703722793,-0.25752166966644485,0.84525765407445586,0.78077791211924596,1.5899361398695,3.3459434962640953,0.30266510321486151]
[36,0.18273885825049341,0.70297388611730971,-0.63452228349901318,0.40594777223461942,0.56741212203905245,0.20647495722333065,3.1474419646025273,-0.16098400933056833]
[37,0.12050005291704391,0.48699160733047131,-0.75899989416591218,-2.601678533905738E-2,0.57675771246324448,-9.7021026508291808E-2,1.9281189018371192,3.6825374152785955]
[38,0.64945693361731327,0.11771898978083439,0.29891386723462654,-0.76456202043833121,0.67390458312190316,2.6470042291076434,0.34509229961419097,2.9731887522732832]
[39,0.84523354850406707,0.93147610649873314,0.69046709700813413,0.86295221299746627,1.2214313339680645,{"$error":"#N/A"},{"$error":"#N/A"},1.0435947806680017]
[40,0.96559113278394504,0.52180085869870974,0.93118226556789008,4.3601717397419471E-2,0.86900152146815302,3.0586906170930055,2.0495721737888095,-1.674485057289258]
[41,0.66499232931154673,0.72501602030632817,0.32998465862309345,0.45003204061265634,0.31141871250459108,3.8064690607324714,4.4636568290698353,2.8532667240888512]
[42,0.48716817186481609,0.50203712162708591,-2.5663656270367818E-2,4.0742432541718276E-3,6.7522271125775414E-4,-5.5477125651314578,3.1982399031123734,1.8694642991698489]
[43,0.77210315614728597,0.45847626516131068,0.54420631229457195,-8.3047469677378638E-2,0.30305739256107228,5.0550472462284537,1.5337908844269625,6.0303583683009405]
[44,0.82636627627465631,0.2765273183663941,0.65273255254931262,-0.44694536326721179,0.6258199429036011,3.5977160775891699,0.90599635347279839,1.4187176768119363]
[45,0.30996283637913491,0.15196584628760113,-0.38007432724173018,-0.69606830742479775,0.62896758282947651,1.0769897987974333,0.30959866942480563,1.9286353210186262]
[46,0.1840653161997976,0.40443685419245889,-0.6318693676004048,-0.19112629161508221,0.43578815705826895,-0.46734735257250426,1.2536828436321694,0.65206520031469761]
[47,0.58275788798882977,0.51568403043388444,0.16551577597765954,3.1368060867768888E-2,2.8379427340090833E-2,7.2448740806163849,2.9939930404384199,0.79605653582915825]
[48,0.3211056530871087,0.88707475191810981,-0.3577886938257826,0.77414950383621961,0.72732020371942463,1.3304431850033636,3.4487240236053922,-0.86559142302577952]
[49,0.94059973373021577,0.12199706419429013,0.88119946746043154,-0.75600587161141974,1.3480573793634907,{"$error":"#N/A"},{"$error":"#N/A"},1.8209270454291122]
[50,0.14907620621989892,0.5485823647611463,-0.70184758756020216,9.7164729522292603E-2,0.50203102082721596,-0.32574214580654726,2.3219788890654351,0.87765012350675176]
[51,0.38302044178353878,0.54107979941368844,-0.23395911643292244,8.215959882737689E-2,6.1487067841549267E-2,-2.4566831341223399,3.5650567671091729,2.2154673609496212]
[52,8.4815952479745493E-2,1.6353855701170983E-2,-0.83036809504050901,-0.96729228859765803,1.6251655448416988,{"$error":"#N/A"},{"$error":"#N/A"},3.8685221851578566]
[53,0.84221407414122895,0.4652930510870229,0.6844281482824579,-6.9413897825954196E-2,0.47326017937274617,4.4339160687633088,1.7531550948948389,3.3489687312365928]
[54,0.40498559499715014,0.64175961031266415,-0.19002881000569971,0.28351922062532831,0.11649409709617589,-0.30899554275172791,5.4449756154800504,0.30563674322353651]
[55,0.31192254229901473,0.384294644489242,-0.37615491540197055,-0.231410711021516,0.19504343755654718,-1.0799446268072685,0.10521637013643548,0.89398330151893313]
[56,7.3945219604894419E-2,0.26715954448559143,-0.85210956079021116,-0.46568091102881715,0.94294941448671565,1.3984482868641281,1.6712498454491269,2.5700818477932006]
[57,0.41540561914582874,0.43564406875484152,-0.16918876170834252,-0.12871186249031696,4.5191580634128571E-2,-1.9613885092742578,-1.0136617109083579,5.0134012454317123]
[58,0.94334481547755944,0.64841364201228391,0.88668963095511888,0.29682728402456782,0.87432493818472645,2.98293172798863,2.3290451867426971,0.69981989225600483]
[59,0.6294690698059815,0.31342593702642774,0.25893813961196299,-0.37314812594714453,0.20628848404357047,4.0259234095517726,-0.91949855173736372,0.88310718913765296]
[60,0.21751765244325438,8.4241915546240942E-2,-0.56496469511349123,-0.83151616890751812,1.0106042458793163,{"$error":"#N/A"},{"$error":"#N/A"},4.4662081817208037]
[61,0.81132182231923589,0.68530048572932756,0.62264364463847177,0.37060097145865512,0.52503018825477843,3.9509058823783221,3.1611900666770865,3.7298517886594404]
[62,0.47641953418452843,0.49373831416690117,-4.7160931630943148E-2,-1.2523371666197658E-2,2.3809883101882164E-3,-4.7185541446383379,0.21591839467451268,6.1958710722807346]
[63,0.92308615531225435,0.82856125921562329,0.84617231062450871,0.65712251843124658,1.1478175834970441,{"$error":"#N/A"},{"$error":"#N/A"},3.5915536804047221]
[64,0.62241658364570296,0.99521523300006831,0.24483316729140592,0.99043046600013662,1.0408957877871894,{"$error":"#N/A"},{"$error":"#N/A"},6.8127581165712234]
[65,0.56290274788396399,0.57439239559870603,0.12580549576792799,0.14878479119741206,3.7963936857071653E-2,5.3029890282387804,5.9063041713248658,3.897793638643237]
[66,0.27617460253729631,0.90514549193163008,{"$f":"-1+2*B69","v":-0.44765079492540738},{"$f":"-1+2*C69","v":0.81029098386326015},{"$f":"D69^2+E69^2","v":0.85696271272743929},{"$f":"IF(OR($F69>1,$F69<0.0000000000001),NA(),$D69*SQRT(-2*LN($F69)/$F69))*$L$8+$L$7","v":1.4626317535270075},{"$f":"IF(OR($F69>1,$F69<0.0000000000001),NA(),$E69*SQRT(-2*LN($F69)/$F69))*$L$8+$L$7","v":2.9726881981836564},{"$f":"Normal_Polar($L$7,$L$8)","v":1.1237951493545966}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.42663573398542542,0.96366195797090493,-0.14672853202914915,0.95017363135174715,2.6321548312726994,1.9037472117265231,5.0180909398273457]
[68,0.17855864253016906,0.92182682930756443,-0.64288271493966187,0.84365365861512887,1.1250496808628829,{"$error":"#N/A"},{"$error":"#N/A"},4.5650984852999699]
[69,0.14106716857892998,0.41316596081555601,-0.71786566284214004,-0.17366807836888798,0.54549171133212726,-0.14020145188978361,1.4822364507581458,2.726147334024966]
[70,0.78799892820694739,0.10465423467224733,0.57599785641389478,-0.79069153065550535,0.9569666272437477,2.3492838079627085,1.5205264296109362,3.1021245604597341]
[71,0.62019869479720879,3.7197902037881203E-2,0.24039738959441759,-0.92560419592423759,0.91453403243636466,2.2125197184075627,1.1817334480771522,3.3371382915666299]
[72,0.32070616340267466,0.34771751832010722,-0.35858767319465068,-0.30456496335978556,0.22134493627350113,-0.64734764777556197,-0.24851382135409805,1.187516474661676]
[73,0.71916827005391148,0.62919972857465234,0.43833654010782297,0.25839945714930468,0.25890920184875243,4.8323782773542554,3.6696874258527288,1.3853748130892751]
[74,0.70290736382840724,0.33028691321614589,0.40581472765681448,-0.33942617356770821,0.27989572048599048,4.4481980507763037,-4.7689351515256106E-2,1.7368739550385546]
[75,0.154172834186179,0.82934810072780096,-0.69165433162764201,0.65869620145560193,0.91226640027131911,1.3793460436390979,2.5910790763230702,-1.1430038544381822]
[76,0.27977295388613965,0.2479116645837256,-0.44045409222772069,-0.5041766708325488,0.44819392277193776,0.33297119765979533,9.1794249214700141E-2,1.2446991122123929]
[77,0.42321062277449939,0.11691194355116818,-0.15357875445100122,-0.76617611289766363,0.61061226979369432,1.609567561354067,5.2204491042828316E-2,2.7228405369717743]
[78,0.98136142771892321,0.2126052668686973,0.96272285543784641,-0.57478946626260541,1.2572182269088512,{"$error":"#N/A"},{"$error":"#N/A"},3.0788002433237018]
[79,0.20085756040090119,0.54482783306965632,-0.59828487919819762,8.965566613931264E-2,0.36598293514808583,-0.80441352558770607,2.4202539149971911,1.8061258317935376]
[80,0.16133779816984994,4.8198744566575136E-2,-0.67732440366030011,-0.90360251086684973,1.2752658454386565,{"$error":"#N/A"},{"$error":"#N/A"},2.5166386190427446]
[81,0.25863578352871763,0.42254787054736553,-0.48272843294256473,-0.15490425890526893,0.25702206939817479,-1.1391162813188727,0.99267901372401779,4.8083116941453374]
[82,0.8347220398143228,0.39308391964321521,0.66944407962864561,-0.21383216071356959,0.49387956870527822,4.263007886010854,1.2771556569056823,0.92847978859573077]
[83,0.51591167107959424,0.85182300536064515,3.1823342159188472E-2,0.70364601072129029,0.49613043351016695,2.1069857568824744,4.3655623805249775,4.8329962168936227]
[84,0.24633192212221666,0.11812905311926203,-0.50733615575556668,-0.76374189376147594,0.84069165522320222,1.3480562421952884,1.0185663793856663,0.90147759430263608]
[85,0.59063871388364364,0.42056439810769575,0.18127742776728728,-0.15887120378460851,5.8101565209894658E-2,5.5882185368419783,-1.1447081162368722,-1.4388023976469868]
[86,0.65393134749071002,1.4831636671858162E-2,0.30786269498142005,-0.97033672665628368,1.0363328020592544,{"$error":"#N/A"},{"$error":"#N/A"},1.3010230111766765]
[87,0.56445460206933995,0.36716035465117058,0.1289092041386799,-0.26567929069765883,8.7203068417278956E-2,3.9284787219001069,-1.9745560635744606,3.8508975145168067]
[88,0.10565266639072934,0.2451461442845756,-0.78869466721854131,-0.50970771143084881,0.88184122919103913,1.1576335894807819,1.4556059865268534,-0.47017823056514363]
[89,0.59226465879030998,0.20324185152060736,0.18452931758061997,-0.59351629695878527,0.38631266380243828,2.8189471311677465,-0.63404468768679489,0.90939602246850382]
[90,0.72089126375496948,0.6153593343442274,0.44178252750993896,0.23071866868845481,0.24840290569444295,4.9587242060657779,3.5451786056080365,4.0161812771774219]
[91,0.58803803186325454,0.23156698246912066,0.17607606372650908,-0.53686603506175867,0.3192279198203552,2.9418882925206273,-0.87187152174227345,3.095793251503248]
[92,0.76602838211191659,0.24775133853500109,0.53205676422383319,-0.50449732292999783,0.53760194919987014,3.61693040994458,0.46682324512658835,1.3052112236187638]
[93,0.48285856602942256,1.9371888135073734E-2,-3.4282867941154871E-2,-0.96125622372985253,0.92518884269364698,1.9718889004188174,1.2117937894028108,3.4638932369974649]
[94,0.62864718503333628,0.85525903591075469,0.25729437006667255,0.71051807182150939,0.57103632325296139,2.720866217865725,3.9906711329381048,4.9523495791523882]
[95,0.33779794281158637,0.96600502897790752,-0.32440411437682726,0.93201005795581504,0.97388077755541524,1.8487394113510267,2.4345702897880086,0.25933253211233631]
[96,0.47576831339143399,0.12342088429061493,-4.8463373217132011E-2,-0.75315823141877014,0.56959602009743271,1.8637416985386923,-0.1175591902143136,0.35429480820040427]
[97,5.6312473117793416E-2,0.82615584090670624,-0.88737505376441317,0.65231168181341248,1.2129450162736379,{"$error":"#N/A"},{"$error":"#N/A"},4.8996975478053821]
[98,0.80804733641082538,0.26781166835787318,0.61609467282165076,-0.46437666328425364,0.595218331282234,3.6269176902720011,0.77372319259552769,1.7653123524997387]
[99,0.49894266970018275,0.59543950981597049,-2.1146605996344991E-3,0.19087901963194098,3.6439271925102559E-2,1.942976603902107,7.1471947532057758,-1.4323457060240825]
[100,0.32081795804802316,0.15219174065625574,-0.35836408390395369,-0.69561651868748853,0.61230715770322108,1.0927777203291602,0.23900097078507998,1.0806248112926715]

{"sheet":"Pareto","index":22,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[14,6,14,8],[0,0,0,5],[4,6,4,9],[9,6,9,8],[10,6,10,8],[11,6,11,8],[12,6,12,8]]}
["UNIVARIATE PARETO"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Pareto\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7/(($B4)^(1/$H$8))","v":3.8583766479651231},{"$f":"Pareto($H$7,$H$8,$B4)","v":3.8583766479651231},{"$f":"Pareto($H$7,$H$8)","v":6.7019895171092339}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7/(($B5)^(1/$H$8))","v":2.2448198592210948},2.2448198592210948,2.0870409612543281,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,2.2059683515380075,2.2059683515380075,3.8620655407560691,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,2.4521946745391587,2.4521946745391587,2.1717813151822041,null,"mu = ",2,"Location","Real number greater than zero"]
[5,0.86717342695468203,2.1477168037341237,2.1477168037341237,10.418564413193602,null,"alpha = ",2,"Shape","Real number greater than zero"]
[6,0.27994300504477809,3.7800294686189457,3.7800294686189457,2.6357334778773045]
[7,0.93667220783619842,2.0665036584120746,2.0665036584120746,2.4555395127411517,null,"Distribution Type:",null,null,"Continuous"]
[8,0.43191155671140469,3.0432146316110944,3.0432146316110944,11.000294645047788,null,"Distrbution Name:",null,null,"Pareto"]
[9,0.96203701528155405,2.0390792468347958,2.0390792468347958,3.0683860353326926,null,"Variate Number:",null,null,"Univariate"]
[10,0.14240354575933512,5.2999234164083839,5.2999234164083839,2.1943008106514168,null,"Simulation Method:",null,null,"Inverse Transform"]
[11,0.20171971836271319,4.4530320314228682,4.4530320314228682,3.739807747627625]
[12,0.58041618261550787,2.6251869664570546,2.6251869664570546,2.1301053591826946,null,"Macro Format:",null,null,"=Pareto(mu, alpha, [unif])"]
[13,0.34366851316718994,3.4116158518683086,3.4116158518683086,3.4916819221339033]
[14,0.9651686825697714,2.0357684752461638,2.0357684752461638,2.0030516350349732,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[15,0.38704808829902526,3.2147524227720896,3.2147524227720896,2.3614621464217684,null,null,null,null,"your own uniform random variable (unif). If"]
[16,0.86385756571325945,2.1518347916930973,2.1518347916930973,2.9115583794388158,null,null,null,null,"not provided, the function will generate one"]
[17,0.17476282037902591,4.784157549922945,4.784157549922945,3.1738590023308646,null,null,null,null,"to be used in the formula."]
[18,0.38117659587117037,3.2394171870018478,3.2394171870018478,5.4267687683543171,null,null,null,null,"2. Column C shows the formula used in the"]
[19,0.87794506028866293,2.1345008193238035,2.1345008193238035,2.1198127893978378,null,null,null,null,"macro directly in the cell.  Column D generates"]
[20,0.18238019015349183,4.6831833771599838,4.6831833771599838,2.0247152739259695,null,null,null,null,"the random variable with the macro, using the"]
[21,0.39753335201985007,3.1720732701284318,3.1720732701284318,4.2121492146016575,null,null,null,null,"same uniform random variable (column A) as"]
[22,0.74199757940000399,2.3218210882627934,2.3218210882627934,2.9248406946320893,null,null,null,null,"used in Column C, and therefore the output of"]
[23,0.57082894586967958,2.6471405571037669,2.6471405571037669,3.35159768873207,null,null,null,null,"Columns C and D will match.  Column E runs"]
[24,0.90195869363590486,2.1058947951440441,2.1058947951440441,2.2941261368780004,null,null,null,null,"the macro using an internally generated "]
[25,0.43843055863807978,3.0205051964448089,3.0205051964448089,2.6542929706503422,null,null,null,null,"uniform random input."]
[26,0.3929492390413114,3.1905221910690522,3.1905221910690522,6.9303209984503571]
[27,0.2515715048326993,3.9874869236125607,3.9874869236125607,2.4634264148818499]
[28,0.30550021398012439,3.6184638340269575,3.6184638340269575,2.0948251241852711]
[29,7.9387447484473794E-2,7.0982955244020651,7.0982955244020651,5.2251996788655957]
[30,0.82057811417206794,2.2078523715848992,2.2078523715848992,2.1277589763969282]
[31,5.0767455327721533E-3,28.069669424625413,28.069669424625413,2.6422350601160698]
[32,2.9980457362279278E-2,11.550768204661383,11.550768204661383,5.2780579925069109]
[33,0.89698739215075429,2.1117223979864557,2.1117223979864557,2.2240304689103065]
[34,4.8518018441997213E-2,9.0798456942409267,9.0798456942409267,6.6431254609337698]
[35,0.37123916516677757,3.2824876590661587,3.2824876590661587,2.7205553179643571]
[36,0.18273885825049341,4.6785851939883552,4.6785851939883552,2.0970641176086757]
[37,0.12050005291704391,5.7615107540858856,5.7615107540858856,2.7759735465496473]
[38,0.64945693361731327,2.4817316353575891,2.4817316353575891,4.6187448917530585]
[39,0.84523354850406707,2.1754125638585786,2.1754125638585786,2.8278815652371647]
[40,0.96559113278394504,2.0353230978579759,2.0353230978579759,4.3516564961734714]
[41,0.66499232931154673,2.4525715030272019,2.4525715030272019,3.811663488960277]
[42,0.48716817186481609,2.8654348743806777,2.8654348743806777,2.7708745336875258]
[43,0.77210315614728597,2.2761052042988386,2.2761052042988386,2.3860829557366285]
[44,0.82636627627465631,2.2001064940104156,2.2001064940104156,3.7439603544541868]
[45,0.30996283637913491,3.5923213754888166,3.5923213754888166,5.809763972134073]
[46,0.1840653161997976,4.6616967115896273,4.6616967115896273,2.1023402734047036]
[47,0.58275788798882977,2.6199072417595426,2.6199072417595426,3.569176704701027]
[48,0.3211056530871087,3.529441760335176,3.529441760335176,3.2628403688796559]
[49,0.94059973373021577,2.0621847454193665,2.0621847454193665,2.8595570064914808]
[50,0.14907620621989892,5.1799531243721049,5.1799531243721049,4.3582027529438152]
[51,0.38302044178353878,3.2316105645957078,3.2316105645957078,4.4285370726497879]
[52,8.4815952479745493E-2,6.8673822857297733,6.8673822857297733,2.0274089640500867]
[53,0.84221407414122895,2.1793086787655698,2.1793086787655698,2.680829217048049]
[54,0.40498559499715014,3.142752696340342,3.142752696340342,2.3399131937405246]
[55,0.31192254229901473,3.5810189130014694,3.5810189130014694,2.674924408274665]
[56,7.3945219604894419E-2,7.3548690400213355,7.3548690400213355,2.2140122485929177]
[57,0.41540561914582874,3.1030860019953357,3.1030860019953357,2.2435744377415192]
[58,0.94334481547755944,2.0591821371384724,2.0591821371384724,2.0957546172524131]
[59,0.6294690698059815,2.520825585549868,2.520825585549868,2.6790640279892517]
[60,0.21751765244325438,4.2882761232246267,4.2882761232246267,4.0058224722504407]
[61,0.81132182231923589,2.2204112390601289,2.2204112390601289,2.0290622393307927]
[62,0.47641953418452843,2.8975785338207687,2.8975785338207687,2.1407386118686542]
[63,0.92308615531225435,2.0816555895610924,2.0816555895610924,4.6693869887504338]
[64,0.62241658364570296,2.5350668600256743,2.5350668600256743,5.4280623658254825]
[65,0.56290274788396399,2.6657125173607139,2.6657125173607139,6.2270511693702586]
[66,0.27617460253729631,{"$f":"$H$7/(($B69)^(1/$H$8))","v":3.8057313415952403},{"$f":"Pareto($H$7,$H$8,$B69)","v":3.8057313415952403},{"$f":"Pareto($H$7,$H$8)","v":3.0285481721440055}]
[{"$f":"A69+1","v":67},0.98183097898545246,2.0184204152420966,2.0184204152420966,2.96890098682421]
[68,0.17855864253016906,4.7330332764374932,4.7330332764374932,2.0178188858523347]
[69,0.14106716857892998,5.3249682286479354,5.3249682286479354,4.6805804570994862]
[70,0.78799892820694739,2.2530310775199371,2.2530310775199371,2.6559279551016353]
[71,0.62019869479720879,2.5395956335380538,2.5395956335380538,2.8309175800151416]
[72,0.32070616340267466,3.5316393120552583,3.5316393120552583,2.3929818474999212]
[73,0.71916827005391148,2.358385177835232,2.358385177835232,2.0467112335149378]
[74,0.70290736382840724,2.3855083942006248,2.3855083942006248,2.732524200030642]
[75,0.154172834186179,5.0936144343775371,5.0936144343775371,2.6637993958532604]
[76,0.27977295388613965,3.7811780799042647,3.7811780799042647,2.2781732672558719]
[77,0.42321062277449939,3.0743387251469967,3.0743387251469967,2.4126025379862157]
[78,0.98136142771892321,2.0189032335469439,2.0189032335469439,2.2022110903601715]
[79,0.20085756040090119,4.4625788614786472,4.4625788614786472,5.8952264701931849]
[80,0.16133779816984994,4.9792270787213155,4.9792270787213155,2.4197347164303404]
[81,0.25863578352871763,3.9326535619890088,3.9326535619890088,2.1315989056579565]
[82,0.8347220398143228,2.1890670063578046,2.1890670063578046,2.024193654614189]
[83,0.51591167107959424,2.784468564921915,2.784468564921915,3.1510423951012054]
[84,0.24633192212221666,4.0296715377361521,4.0296715377361521,3.1320140736334197]
[85,0.59063871388364364,2.6023699821341038,2.6023699821341038,3.3441623851762556]
[86,0.65393134749071002,2.4732266488811741,2.4732266488811741,6.4168495107852266]
[87,0.56445460206933995,2.6620455755466836,2.6620455755466836,2.2851207143372121]
[88,0.10565266639072934,6.1530403726706506,6.1530403726706506,4.2755449962460528]
[89,0.59226465879030998,2.5987953823303847,2.5987953823303847,2.1064666362583377]
[90,0.72089126375496948,2.3555651174897876,2.3555651174897876,2.0360276633516494]
[91,0.58803803186325454,2.6081183095526419,2.6081183095526419,5.0877061253751412]
[92,0.76602838211191659,2.2851123904776243,2.2851123904776243,5.7942833985056961]
[93,0.48285856602942256,2.8781937482376803,2.8781937482376803,3.332721384265291]
[94,0.62864718503333628,2.5224728938373162,2.5224728938373162,2.0771359936711722]
[95,0.33779794281158637,3.4411332932883085,3.4411332932883085,2.6759734326354678]
[96,0.47576831339143399,2.8995609253243657,2.8995609253243657,2.259720632614016]
[97,5.6312473117793416E-2,8.4280614834331615,8.4280614834331615,2.6162787733140824]
[98,0.80804733641082538,2.2249056257269832,2.2249056257269832,9.0677685848651706]
[99,0.49894266970018275,2.8314224578687548,2.8314224578687548,3.4985029659158493]
[100,0.32081795804802316,3.5310239276046294,3.5310239276046294,2.0554245638562487]

{"sheet":"Poisson","index":23,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[13,4,13,6],[0,0,0,4],[4,4,4,7],[8,4,8,6],[9,4,9,6],[10,4,10,6],[11,4,11,6]]}
["UNIVARIATE POISSON"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"Poissonrv($F$7)","v":16}]
[{"$f":"A4+1","v":2},12,null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},10,null,null,"Name","Value","Type","Feasible Range"]
[4,11,null,null,"lambda =",10.7,"Shape","Any Finite Positive Real Number"]
[5,9]
[6,12,null,null,"Distribution Type:",null,null,"Discrete"]
[7,6,null,null,"Distrbution Name:",null,null,"Poisson"]
[8,11,null,null,"Variate Number:",null,null,"Univariate"]
[9,10,null,null,"Simulation Method:",null,null,"Convolution"]
[10,10]
[11,17,null,null,"Macro Format:",null,null,"=Poissonrv(lambda)"]
[12,15]
[13,10]
[14,11]
[15,14,null,null,null,null,"Notes:","1. The Poisson distribution does not lend"]
[16,5,null,null,null,null,null,"itself easily to a manual presentation so no"]
[17,5,null,null,null,null,null,"manual example is provided here, only the"]
[18,14,null,null,null,null,null,"output of the macro generated variates."]
[19,7]
[20,12]
[21,17]
[22,9]
[23,8]
[24,11]
[25,19]
[26,19]
[27,14]
[28,13]
[29,9]
[30,16]
[31,9]
[32,13]
[33,12]
[34,9]
[35,7]
[36,18]
[37,12]
[38,8]
[39,11]
[40,17]
[41,7]
[42,12]
[43,13]
[44,10]
[45,14]
[46,7]
[47,10]
[48,12]
[49,9]
[50,12]
[51,14]
[52,12]
[53,17]
[54,14]
[55,9]
[56,9]
[57,9]
[58,14]
[59,10]
[60,12]
[61,11]
[62,6]
[63,14]
[64,15]
[65,9]
[66,{"$f":"Poissonrv($F$7)","v":13}]
[{"$f":"A69+1","v":67},5]
[68,15]
[69,12]
[70,7]
[71,9]
[72,11]
[73,7]
[74,9]
[75,11]
[76,9]
[77,12]
[78,15]
[79,7]
[80,16]
[81,8]
[82,12]
[83,9]
[84,15]
[85,12]
[86,10]
[87,17]
[88,12]
[89,13]
[90,7]
[91,13]
[92,9]
[93,6]
[94,11]
[95,12]
[96,12]
[97,14]
[98,10]
[99,7]
[100,13]

{"sheet":"Rayleigh","index":24,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[13,6,13,8],[0,0,0,5],[4,6,4,9],[8,6,8,8],[9,6,9,8],[10,6,10,8],[11,6,11,8]]}
["UNIVARIATE RAYLEIGH"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Rayleigh\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7*SQRT(-2*LN($B4))","v":3.2424666090757226},{"$f":"Rayleigh($H$7,$B4)","v":3.2424666090757226},{"$f":"Rayleigh($H$7)","v":3.0257649416096197}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7*SQRT(-2*LN($B5))","v":1.3592827316394671},1.3592827316394671,0.99078307151720812,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,1.2523219626331341,1.2523219626331341,0.29028095367158452,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,1.8059290287116574,1.8059290287116574,0.99142686124905754,null,"sigma = ",2,"Scale","Real number greater than zero"]
[5,0.86717342695468203,1.0677688555695841,1.0677688555695841,3.1494986579872211]
[6,0.27994300504477809,3.1914501405401299,3.1914501405401299,3.5089607668046257,null,"Distribution Type:",null,null,"Continuous"]
[7,0.93667220783619842,0.72344669188874478,0.72344669188874478,2.2012625793747085,null,"Distrbution Name:",null,null,"Rayleigh"]
[8,0.43191155671140469,2.5915778074875568,2.5915778074875568,3.1963143863107986,null,"Variate Number:",null,null,"Univariate"]
[9,0.96203701528155405,0.55643401501356671,0.55643401501356671,4.7355543069716726,null,"Simulation Method:",null,null,"Inverse Transform"]
[10,0.14240354575933512,3.9487622165118332,3.9487622165118332,2.222581892850827]
[11,0.20171971836271319,3.5786881148866598,3.5786881148866598,3.2096993227197266,null,"Macro Format:",null,null,"=Rayleigh(sigma, [unif])"]
[12,0.58041618261550787,2.0861637069576773,2.0861637069576773,5.3183245794841429]
[13,0.34366851316718994,2.9231184864213824,2.9231184864213824,1.3829016545323889,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[14,0.9651686825697714,0.53255904708159851,0.53255904708159851,2.5032690823755517,null,null,null,null,"your own uniform random variable (unif). If"]
[15,0.38704808829902526,2.755657938861467,2.755657938861467,4.6134665321393278E-2,null,null,null,null,"not provided, the function will generate one"]
[16,0.86385756571325945,1.0820254276739347,1.0820254276739347,0.85767317255810016,null,null,null,null,"to be used in the formula."]
[17,0.17476282037902591,3.7355862045410064,3.7355862045410064,2.9668993249161346,null,null,null,null,"2. Column C shows the formula used in the"]
[18,0.38117659587117037,2.7777580960446793,2.7777580960446793,2.8544629342753431,null,null,null,null,"macro directly in the cell.  Column D generates"]
[19,0.87794506028866293,1.0204754225671626,1.0204754225671626,3.6142937198253784,null,null,null,null,"the random variable with the macro, using the"]
[20,0.18238019015349183,3.6896198328333605,3.6896198328333605,4.02653993696926,null,null,null,null,"same uniform random variable (column A) as"]
[21,0.39753335201985007,2.7165808568199536,2.7165808568199536,1.2363851104649963,null,null,null,null,"used in Column C, and therefore the output of"]
[22,0.74199757940000399,1.5450807049063122,1.5450807049063122,1.7874012507948476,null,null,null,null,"Columns C and D will match.  Column E runs"]
[23,0.57082894586967958,2.1178586989903154,2.1178586989903154,0.32455014273722982,null,null,null,null,"the macro using an internally generated "]
[24,0.90195869363590486,0.90856614140447467,0.90856614140447467,0.35547676786503607,null,null,null,null,"uniform random input."]
[25,0.43843055863807978,2.5683517529419202,2.5683517529419202,0.69239414322415094]
[26,0.3929492390413114,2.7336054407318642,2.7336054407318642,5.1307524260117932]
[27,0.2515715048326993,3.3226832727801865,3.3226832727801865,1.5463947366261732]
[28,0.30550021398012439,3.0800062336882283,3.0800062336882283,2.9429594292080754]
[29,7.9387447484473794E-2,4.5019240467711281,4.5019240467711281,1.7984870265842106]
[30,0.82057811417206794,1.2577636339114453,1.2577636339114453,2.163431928726339]
[31,5.0767455327721533E-3,6.501129050155118,6.501129050155118,1.5639722873033612]
[32,2.9980457362279278E-2,5.296949711556155,5.296949711556155,1.4884321096763633]
[33,0.89698739215075429,0.93258124619967142,0.93258124619967142,2.5550839631955111]
[34,4.8518018441997213E-2,4.9200162892129153,4.9200162892129153,2.8645354762119837]
[35,0.37123916516677757,2.8155408347627464,2.8155408347627464,3.5255944873217242]
[36,0.18273885825049341,3.6874892806638884,3.6874892806638884,1.6567109472455233]
[37,0.12050005291704391,4.1144672431856169,4.1144672431856169,3.4528057949382203]
[38,0.64945693361731327,1.8582115101325147,1.8582115101325147,2.0528492149705571]
[39,0.84523354850406707,1.159801021041424,1.159801021041424,2.5778271444315273]
[40,0.96559113278394504,0.52926207010288462,0.52926207010288462,1.5567151001173634]
[41,0.66499232931154673,1.8066095831975753,1.8066095831975753,1.8480931273849674]
[42,0.48716817186481609,2.3985760665947744,2.3985760665947744,6.2448661279307824]
[43,0.77210315614728597,1.4384355833516795,1.4384355833516795,2.9421735886384046]
[44,0.82636627627465631,1.2352074157882651,1.2352074157882651,1.1732799596268548]
[45,0.30996283637913491,3.0611146614753211,3.0611146614753211,4.7071297758199213]
[46,0.1840653161997976,3.679635422176156,3.679635422176156,2.8302612149530795]
[47,0.58275788798882977,2.0784291479009065,2.0784291479009065,4.7641208056058657]
[48,0.3211056530871087,3.0146111824418305,3.0146111824418305,1.9100139299388106]
[49,0.94059973373021577,0.69992909673060366,0.69992909673060366,4.5834123435460077]
[50,0.14907620621989892,3.902099591392278,3.902099591392278,1.0563922562923398]
[51,0.38302044178353878,2.7708004885560347,2.7708004885560347,4.0108917100021886]
[52,8.4815952479745493E-2,4.4427663769426289,4.4427663769426289,2.460985113888047]
[53,0.84221407414122895,1.1720786739165114,1.1720786739165114,1.2165034788362488]
[54,0.40498559499715014,2.6890946884279434,2.6890946884279434,1.8804019046910136]
[55,0.31192254229901473,3.0528680074406944,3.0528680074406944,0.96186954746173825]
[56,7.3945219604894419E-2,4.564586058364366,4.564586058364366,2.327888183189577]
[57,0.41540561914582874,2.6510372921697294,2.6510372921697294,3.0711383735100113]
[58,0.94334481547755944,0.68307191540979983,0.68307191540979983,3.6025082469037839]
[59,0.6294690698059815,1.924325463629488,1.924325463629488,1.8445413461703217]
[60,0.21751765244325438,3.4933940757814375,3.4933940757814375,1.0516733410433488]
[61,0.81132182231923589,1.2933382604023629,1.2933382604023629,4.5415182079924419]
[62,0.47641953418452843,2.4354982054532681,2.4354982054532681,3.6693078869898801]
[63,0.92308615531225435,0.80016351396587149,0.80016351396587149,1.1233825094210896]
[64,0.62241658364570296,1.9476050149821358,1.9476050149821358,1.9314984060990843]
[65,0.56290274788396399,2.1441052303810535,2.1441052303810535,1.738895203675801]
[66,0.27617460253729631,{"$f":"$H$7*SQRT(-2*LN($B69))","v":3.2083914915665472},{"$f":"Rayleigh($H$7,$B69)","v":3.2083914915665472},{"$f":"Rayleigh($H$7)","v":1.9857442838016077}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.38299978695858955,0.38299978695858955,0.81916903049925016]
[68,0.17855864253016906,3.7125066487597733,3.7125066487597733,1.8090458859514669]
[69,0.14106716857892998,3.9583017865072434,3.9583017865072434,3.1450889675012346]
[70,0.78799892820694739,1.3806043582971936,1.3806043582971936,3.227207457385918]
[71,0.62019869479720879,1.9549227643156206,1.9549227643156206,2.9194225485422316]
[72,0.32070616340267466,3.0162625268699879,3.0162625268699879,4.0413759616076952]
[73,0.71916827005391148,1.6239702341803486,1.6239702341803486,2.5458795694508516]
[74,0.70290736382840724,1.6793574211639872,1.6793574211639872,2.2312326232434332]
[75,0.154172834186179,3.86748601131639,3.86748601131639,4.9294375877839673]
[76,0.27977295388613965,3.1922116267329788,3.1922116267329788,1.8229709470329829]
[77,0.42321062277449939,2.6228004844884643,2.6228004844884643,2.2956053928480831]
[78,0.98136142771892321,0.3879634974748245,0.3879634974748245,0.95506286207238789]
[79,0.20085756040090119,3.5834723683705372,3.5834723683705372,4.7696059062986693]
[80,0.16133779816984994,3.820214639739544,3.820214639739544,5.0012460890077906]
[81,0.25863578352871763,3.289175517566131,3.289175517566131,2.9998985522672368]
[82,0.8347220398143228,1.2021863283208234,1.2021863283208234,0.69152827919546356]
[83,0.51591167107959424,2.3009905836084803,2.3009905836084803,0.87083900723046281]
[84,0.24633192212221666,3.3479251790759208,3.3479251790759208,2.7137074491988518]
[85,0.59063871388364364,2.0524146983098692,2.0524146983098692,4.9154955958533861]
[86,0.65393134749071002,1.8433727920110163,1.8433727920110163,3.4277416280173556]
[87,0.56445460206933995,2.1389629638974368,2.1389629638974368,0.80154044670741731]
[88,0.10565266639072934,4.2403757354990388,4.2403757354990388,5.9101322704643948]
[89,0.59226465879030998,2.0470499461062759,2.0470499461062759,1.1305638192478111]
[90,0.72089126375496948,1.6180654280233064,1.6180654280233064,3.9371309443276772]
[91,0.58803803186325454,2.0609971433956433,2.0609971433956433,1.8966435758763116]
[92,0.76602838211191659,1.4602357551095408,1.4602357551095408,5.1348627604586756]
[93,0.48285856602942256,2.4133486978329795,2.4133486978329795,2.2943200934452035]
[94,0.62864718503333628,1.92703937427195,1.92703937427195,2.4241503632728341]
[95,0.33779794281158637,2.9466012483357988,2.9466012483357988,4.2481370973280637]
[96,0.47576831339143399,2.4377436777775179,2.4377436777775179,1.3768641146550931]
[97,5.6312473117793416E-2,4.7973652943999765,4.7973652943999765,5.4931794150628459]
[98,0.80804733641082538,1.3057860085333834,1.3057860085333834,6.1642278754727133]
[99,0.49894266970018275,2.3584131617872539,2.3584131617872539,1.2998430980629678]
[100,0.32081795804802316,3.0158002925974396,3.0158002925974396,0.42483080885625701]

{"sheet":"Stable","index":25,"n_rows":103,"n_cols":13,"rows_kept":103,"cut":false,"hidden":false,"merged":[[19,9,19,11],[0,0,0,8],[4,9,4,12],[11,9,11,11],[12,9,12,11],[13,9,13,11],[14,9,14,11],[16,9,16,11],[17,9,17,11]]}
["UNIVARIATE STABLE"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate for\nExponential","Uniform\nRandom \nVariate on (0,1)","Uniform\nRandom\nVariate on\n(-pi/2, pi/2)","Exponential\nRandom \nVariate w/\nmean = 1","Stable\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,0.44405580182317539,{"$f":"-PI()/2+PI()*C4","v":-0.17575388200328379},{"$f":"Exponential(1,B4)","v":0.31291719558324704},{"$f":"IF($K$10<>1,$K$8*($M$18*SIN($K$10*($D4+$M$17))/(COS($D4)^(1/$K$10))*(COS($D4-$K$10*($D4+$M$17))/$E4)^((1-$K$10)/$K$10))+$K$7,$K$8*((2/PI())*(((PI()/2)+$K$9*$D4)*TAN($D4)-$K$9*LN(((PI()/2)*$E4*COS($D4))/((PI()/2)+$K$9*$D4))))+(2/PI())*$K$9*$K$8*LN($K$8)+$K$7)","v":0.91598660202519433},{"$f":"Stable($K$7,$K$8,$K$9,$K$10,$B4:$C4)","v":0.91598660202519433},{"$f":"Stable($K$7,$K$8,$K$9,$K$10)","v":47.910419564210564}]
[{"$f":"A4+1","v":2},0.79377423808874648,0.65718795300261768,{"$f":"-PI()/2+PI()*C5","v":0.49382051838584129},{"$f":"Exponential(1,B5)","v":1.5787837786791721},{"$f":"IF($K$10<>1,$K$8*($M$18*SIN($K$10*($D5+$M$17))/(COS($D5)^(1/$K$10))*(COS($D5-$K$10*($D5+$M$17))/$E5)^((1-$K$10)/$K$10))+$K$7,$K$8*((2/PI())*(((PI()/2)+$K$9*$D5)*TAN($D5)-$K$9*LN(((PI()/2)*$E5*COS($D5))/((PI()/2)+$K$9*$D5))))+(2/PI())*$K$9*$K$8*LN($K$8)+$K$7)","v":6.6914775152382342},6.6914775152382333,{"$f":"Stable($K$7,$K$8,$K$9,$K$10)","v":1.6661199868360532},null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,0.22897348669921869,-0.85145490311379091,1.7258613510340279,-7.5087072760829123,-7.5087072760829123,4.1228399295939235,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,0.59746096109928493,0.30618263940131407,1.0942121543105265,4.386902275232571,4.386902275232571,22.577943069718408,null,"mu = ",3,"Location","Any finite real number"]
[5,0.86717342695468203,0.12564729724809154,-1.1760637008168793,2.0187109637239686,-12.121419564171582,-12.121419564171582,28.403297135257766,null,"sigma = ",6,"Scale","Real number greater than zero"]
[6,0.27994300504477809,0.57228225911488473,0.22708141422019579,0.32842491044496619,3.4116390938664005,3.4116390938664005,13.377125753690912,null,"beta = ",0.25,"Skew","Real number between [-1, +1]"]
[7,0.93667220783619842,0.29739908159505091,-0.63648955687153319,2.7594309914679234,-6.7867196960102483,-6.7867196960102483,-2.028954609939535,null,"alpha = ",1.5,"Shape","Real number between (0, +2]"]
[8,0.43191155671140469,0.33552329929780045,-0.51671879461271719,0.56547816236739923,-1.9497546625797453,-1.9497546625797453,-2.0706741310634644]
[9,0.96203701528155405,0.79162900118788981,0.91617952770560374,3.2711436803428628,14.526165355323036,14.526165355323036,-1.8560819294784139,null,"Distribution Type:",null,null,"Continuous"]
[10,0.14240354575933512,0.24822859655358209,-0.79096319145125837,0.15362162318829672,-1.4202928531261971,-1.4202928531261971,57.057815708621121,null,"Distrbution Name:",null,null,"Stable"]
[11,0.20171971836271319,0.14050226564731538,-1.129395441224569,0.22529551307727516,-3.9350732446328385,-3.9350732446328385,11.93553623543281,null,"Variate Number:",null,null,"Univariate"]
[12,0.58041618261550787,0.24325661202272519,-0.8065831415271606,0.86849196997088973,-4.9987677630252065,-4.9987677630252065,6.7702860924116104,null,"Simulation Method:",null,null,"Pseudo-Inverse Transform"]
[13,0.34366851316718994,0.66165916832683569,0.50786725560102264,0.42108930237290998,5.4809679795540092,5.4809679795540092,-16.344087646301801]
[14,0.9651686825697714,0.56279612960791148,0.1972798594500873,3.3572383707364808,3.4746378474860617,3.4746378474860617,-65.176867634683418,null,"B(alpha, beta) = ",null,null,{"$f":"ATAN(K9*TAN(PI()*K10/2))/K10","v":-0.16331910875124281}]
[15,0.38704808829902526,0.97513917603786493,1.492693744873264,0.48946879359295109,28.171517254660884,28.171517254660884,1.4904036686778812,null,"S(alpha, beta) = ",null,null,{"$f":"(1+K9^2*TAN(PI()*K10/2)^2)^(1/(2*K10))","v":1.020413775479337}]
[16,0.86385756571325945,0.43110523880919793,-0.21643927562784704,1.9940536303616458,-1.3127178851426189,-1.3127178851426189,-16.131800103377387]
[17,0.17476282037902591,8.3728507126800911E-2,-1.3077554639092983,0.19208444351525109,-5.1711215472381262,-5.1711215472381244,-5.0007058406573517,null,"Macro Format:",null,null,"=Stable(mu, sigma, beta, alpha, [unif])"]
[18,0.38117659587117037,6.6163538436367908E-2,-1.3629374405076973,0.47993533920008496,-9.245951955412643,-9.245951955412643,-2.4416112568040607]
[19,0.87794506028866293,5.8800603133947305E-2,-1.3860687839626387,2.1032840101122163,-18.097067104058695,-18.097067104058695,7.4616687076417492,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[20,0.18238019015349183,0.91427131754721946,1.3014717277993091,0.20135783056190076,11.839878434894848,11.839878434894848,-6.1413353476516548,null,null,null,null,"the two needed uniform random variables.  If"]
[21,0.39753335201985007,0.99208452571603889,1.5459291309347254,0.50672297119907339,55.706805050303387,55.706805050303373,6.5698964980962842,null,null,null,null,"not provided, the macro will generate the two"]
[22,0.74199757940000399,0.33932002996360344,-0.50479101344537147,1.3547863119340047,-3.5131803055096302,-3.513180305509632,4.9664590646191318,null,null,null,null,"to be used in its calculation."]
[23,0.57082894586967958,0.51026222064659499,3.2239716992860323E-2,0.84589971194833169,1.8584379232458956,1.8584379232458954,-0.81315548609485377,null,null,null,null,"2. The B() and S() calculations above are inter-"]
[24,0.90195869363590486,0.68823388521184869,0.59135419093820829,2.3223663956038276,8.499012617942288,8.4990126179422845,29.548766886900921,null,null,null,null,"mediate calculations for the manual calculation"]
[25,0.43843055863807978,0.3802352804098853,-0.37625196322354593,0.57701984128034978,-0.99935435573218312,-0.99935435573218268,-10.826685400412423,null,null,null,null,"of the Stable variates in the table.  These inter-"]
[26,0.3929492390413114,0.81007583244623871,0.97413195726884316,0.49914286545749886,9.7550445296422978,9.7550445296422978,-50.846464408498079,null,null,null,null,"mediate calculations are done internally by the"]
[27,0.2515715048326993,7.1945023913193018E-2,-1.3447743682068674,0.2897796105244248,-6.9865546253381332,-6.9865546253381332,21.744176606415341,null,null,null,null,"macro and are not necessary to provide."]
[28,0.30550021398012439,6.0405119249104633E-2,-1.381028047922694,0.36456342489451665,-8.6243961123949298,-8.6243961123949298,0.84760184744568656,null,null,null,null,"3. Column C shows the formula used in the"]
[29,7.9387447484473794E-2,0.36390303471752294,-0.42756122630729498,8.2716012545824918E-2,0.71756617460492533,0.71756617460492489,7.2645731730760232,null,null,null,null,"macro directly in the cell.  Column D generates"]
[30,0.82057811417206794,2.3405931264653845E-2,-1.4972644250834324,1.718015342216614,-27.988672941988497,-27.988672941988497,2.9290597685809292,null,null,null,null,"the random variable with the macro, using the"]
[31,5.0767455327721533E-3,0.72094892071410632,0.6941315061340303,5.0896759870231161E-3,3.8986209037983075,3.8986209037983075,157.06309094515564,null,null,null,null,"same uniform random variable (column A) as"]
[32,2.9980457362279278E-2,0.50045935317620716,1.4431005637756122E-3,3.0439060638460996E-2,2.5357362369462786,2.5357362369462781,19.99142612486105,null,null,null,null,"used in Column C, and therefore the output of"]
[33,0.89698739215075429,0.5185423769601476,5.8252595238092342E-2,2.2729038919401852,1.7252216071085624,1.7252216071085624,9.0854853247435301,null,null,null,null,"Columns C and D will match.  Column E runs"]
[34,4.8518018441997213E-2,0.73465611364814176,0.73719392275693396,4.9734529305949592E-2,5.0917535413041382,5.0917535413041382,-19.926985664389676,null,null,null,null,"the macro using an internally generated "]
[35,0.37123916516677757,0.92262882703722793,1.3277276182154267,0.46400432537754199,15.43031114488382,15.43031114488382,6.4957257609452057,null,null,null,null,"uniform random input."]
[36,0.18273885825049341,0.70297388611730971,0.63766126949671165,0.20179660025018376,5.7156504367327248,5.7156504367327248,0.66804148571299393]
[37,0.12050005291704391,0.48699160733047131,-4.0867070845602704E-2,0.12840177497171634,2.0570415111908522,2.0570415111908522,9.2020124664282292]
[38,0.64945693361731327,0.11771898978083439,-1.2009712133114152,1.0482717087782691,-9.4939093154574383,-9.493909315457433,6.8077677527774112]
[39,0.84523354850406707,0.93147610649873314,1.3555221663759474,1.8658380629165308,24.270531689705788,24.270531689705788,3.210237285680583]
[40,0.96559113278394504,0.52180085869870974,6.8489417529815633E-2,3.3694409799106495,1.6869891194594353,1.6869891194594355,-7.8074096408182339]
[41,0.66499232931154673,0.72501602030632817,0.70690867633437238,1.0936018498417437,8.5229916614625232,8.5229916614625232,2.1168156447231352]
[42,0.48716817186481609,0.50203712162708591,6.3998063381220938E-3,0.66780730795547238,1.7396040719686612,1.7396040719686612,9.2820574059616341]
[43,0.77210315614728597,0.45847626516131068,-0.1304506603188369,1.4788621916516949,-4.1387237249898234E-2,-4.1387237249898234E-2,-2.8275773812010465]
[44,0.82636627627465631,0.2765273183663941,-0.702060134898147,1.7508072345314403,-6.0608654292056219,-6.0608654292056237,20.681154868265089]
[45,0.30996283637913491,0.15196584628760113,-1.0933815405012131,0.37100982252115261,-4.9035133031337761,-4.9035133031337743,8.9223026594881745]
[46,0.1840653161997976,0.40443685419245889,-0.30022047682290132,0.20342097158424804,0.5574158639261162,0.5574158639261162,-9.7493715807801102]
[47,0.58275788798882977,0.51568403043388444,4.9272834789770181E-2,0.87408862132549103,1.9944753525177905,1.9944753525177907,4.1031417315855423]
[48,0.3211056530871087,0.88707475191810981,1.2160311970160254,0.38728976454247643,12.236057994213917,12.236057994213917,6.8261132176183317]
[49,0.94059973373021577,0.12199706419429013,-1.1875312461625924,2.8234565699672847,-14.123827355629139,-14.123827355629139,6.8377628150792962]
[50,0.14907620621989892,0.5485823647611463,0.15262600022763695,0.16143270344307428,2.9458553244588099,2.9458553244588099,-0.56293184428862642]
[51,0.38302044178353878,0.54107979941368844,0.12905599604898588,0.48291938655515104,2.750502035628585,2.750502035628585,0.59304939169654025]
[52,8.4815952479745493E-2,1.6353855701170983E-2,-1.5194191738662302,8.8630089102645679E-2,-11.079504760578763,-11.079504760578761,33.555041667902778]
[53,0.84221407414122895,0.4652930510870229,-0.1090350957335251,1.846516064289633,-4.1622824739570241E-2,-4.1622824739570241E-2,-4.033500320461636]
[54,0.40498559499715014,0.64175961031266415,0.44535095033401761,0.51916966364074346,5.1634083807892104,5.1634083807892104,0.8627335217323866]
[55,0.31192254229901473,0.384294644489242,-0.36349909485359255,0.37385386351817024,-0.38246216138049016,-0.38246216138049016,2.7864634707133793]
[56,7.3945219604894419E-2,0.26715954448559143,-0.73148986450256703,7.6821887991662202E-2,-0.29904706234465994,-0.29904706234466083,-4.8059819867444871]
[57,0.41540561914582874,0.43564406875484152,-0.20218012081471981,0.53683703830094498,0.31663411938079955,0.31663411938079999,6.1973544458595722]
[58,0.94334481547755944,0.64841364201228391,0.46625520743829663,2.870771777206,7.117923854393351,7.117923854393351,18.374980290285546]
[59,0.6294690698059815,0.31342593702642774,-0.58613970558817408,0.99281835542540597,-3.5460109677338778,-3.5460109677338778,-9.333545786245999]
[60,0.21751765244325438,8.4241915546240942E-2,-1.3061425437904943,0.24528391585520054,-5.8424412872029308,-5.8424412872029308,4.0318366477696168]
[61,0.81132182231923589,0.68530048572932756,0.58213864467387566,1.6677124788660345,7.8127804064818545,7.8127804064818545,1.3782820399122431]
[62,0.47641953418452843,0.49373831416690117,-1.9671666212350614E-2,0.64706455309941524,1.5486541556347337,1.5486541556347335,-2.008040830916622]
[63,0.92308615531225435,0.82856125921562329,1.0322056382060136,2.5650693837237069,15.771867805814477,15.771867805814477,2.5316361892831547]
[64,0.62241658364570296,0.99521523300006831,1.5557645379387721,0.97396376422847808,93.993833725736636,93.99383372573665,-0.75874622744229292]
[65,0.56290274788396399,0.57439239559870603,0.2337106034958405,0.8275995637580329,3.6187427963952352,3.6187427963952352,-3.5517582475786664]
[66,0.27617460253729631,0.90514549193163008,{"$f":"-PI()/2+PI()*C69","v":1.2728021010874317},{"$f":"Exponential(1,B69)","v":0.32320507940661553},{"$f":"IF($K$10<>1,$K$8*($M$18*SIN($K$10*($D69+$M$17))/(COS($D69)^(1/$K$10))*(COS($D69-$K$10*($D69+$M$17))/$E69)^((1-$K$10)/$K$10))+$K$7,$K$8*((2/PI())*(((PI()/2)+$K$9*$D69)*TAN($D69)-$K$9*LN(((PI()/2)*$E69*COS($D69))/((PI()/2)+$K$9*$D69))))+(2/PI())*$K$9*$K$8*LN($K$8)+$K$7)","v":12.721496913703596},{"$f":"Stable($K$7,$K$8,$K$9,$K$10,$B69:$C69)","v":12.721496913703596},{"$f":"Stable($K$7,$K$8,$K$9,$K$10)","v":8.9394369068545387}]
[{"$f":"A69+1","v":67},0.98183097898545246,0.42663573398542542,-0.23048063914739481,4.0080372772469737,-2.6373726019475514,-2.6373726019475523,3.9855589024033762]
[68,0.17855864253016906,0.92182682930756443,1.32520806803972,0.19669472875175081,12.279405967543532,12.279405967543532,3.5410490641171086]
[69,0.14106716857892998,0.41316596081555601,-0.27279717958337746,0.15206455397710658,0.90956402639103917,0.90956402639103917,35.143578221415204]
[70,0.78799892820694739,0.10465423467224733,-1.242015351981502,1.5511639486952975,-11.95118507327345,-11.951185073273447,17.993978226589519]
[71,0.62019869479720879,3.7197902037881203E-2,-1.4539356710237361,0.96810704405695702,-17.15767950156744,-17.157679501567436,4.7030082349870845]
[72,0.32070616340267466,0.34771751832010722,-0.4784095257159735,0.38670149599353032,-1.1277593444033487,-1.1277593444033496,0.93826705473456329]
[73,0.71916827005391148,0.62919972857465234,0.40589291813592299,1.2699996148308113,5.4974752032623826,5.4974752032623826,-0.74532562673803948]
[74,0.70290736382840724,0.33028691321614589,-0.53316938665820302,1.2137112825104366,-3.5308815012472232,-3.5308815012472232,2.5799161089165499]
[75,0.154172834186179,0.82934810072780096,1.0346775737202107,0.1674402359754727,8.162543708464705,8.162543708464705,-2.5728189840517128]
[76,0.27977295388613965,0.2479116645837256,-0.79195886259944737,0.32818877485701314,-2.6987227510284075,-2.6987227510284075,11.598853221284234]
[77,0.42321062277449939,0.11691194355116818,-1.203506623817642,0.55027810991902437,-7.1077487802051955,-7.1077487802051973,-4.1151384229848915]
[78,0.98136142771892321,0.2126052668686973,-0.90287718228569969,3.9825220670210228,-11.584299546060274,-11.584299546060274,6.2200176305007426]
[79,0.20085756040090119,0.54482783306965632,0.1408307910479818,0.22421607676518993,2.8730751467100815,2.8730751467100815,-8.0565094436857745]
[80,0.16133779816984994,4.8198744566575136E-2,-1.4193755049522931,0.17594727357602225,-7.092987351243492,-7.0929873512434956,9.5599862994926177E-3]
[81,0.25863578352871763,0.42254787054736553,-0.24332304089328205,0.29926325423837807,0.55137070430248558,0.55137070430248558,-1.2745997994293683]
[82,0.8347220398143228,0.39308391964321521,-0.33588677259949118,1.8001266152547473,-2.4248156702633308,-2.4248156702633299,13.437483940844201]
[83,0.51591167107959424,0.85182300536064515,1.1052845690048851,0.72548789114676404,12.417016662789658,12.41701666278966,9.2641851661822745]
[84,0.24633192212221666,0.11812905311926203,-1.1996829613399045,0.28280322291345938,-5.0612241689520197,-5.0612241689520197,14.538886059814772]
[85,0.59063871388364364,0.42056439810769575,-0.24955430333834649,0.89315717271684258,-0.57761421904897592,-0.57761421904897681,-11.999471923628558]
[86,0.65393134749071002,1.4831636671858162E-2,-1.524201365985874,1.0611181059496853,-31.069979682062112,-31.069979682062097,-5.4870617917505253]
[87,0.56445460206933995,0.36716035465117058,-0.41732805393335592,0.83115624488335493,-1.8440391010013721,-1.8440391010013721,0.26493297495274071]
[88,0.10565266639072934,0.2451461442845756,-0.80064700085461038,0.11166106292008815,-1.0132259560861669,-1.0132259560861678,-0.43236223768323612]
[89,0.59226465879030998,0.20324185152060736,-0.9322932191557689,0.89713698856332225,-6.1219483285942502,-6.1219483285942502,7.2293789296707365]
[90,0.72089126375496948,0.6153593343442274,0.36241203729883353,1.2761538374427104,5.0447520776088899,5.0447520776088899,-1.0115435559333594]
[91,0.58803803186325454,0.23156698246912066,-0.84330719585595071,0.88682424424117823,-5.3508713528242797,-5.3508713528242797,-22.637794617336517]
[92,0.76602838211191659,0.24775133853500109,-0.79246254173629938,1.4525554620573597,-6.3612598779463685,-6.3612598779463685,1.8313700486450228]
[93,0.48285856602942256,1.9371888135073734E-2,-1.5099377453435856,0.6594388752120165,-21.982143258886651,-21.982143258886648,5.9377161701278407]
[94,0.62864718503333628,0.85525903591075469,1.1160791773386194,0.99060268453562239,13.632156995307328,13.632156995307328,0.11188041972914675]
[95,0.33779794281158637,0.96600502897790752,1.4639979755728931,0.41218454727699749,22.611584628223255,22.611584628223259,1.9790122097856391]
[96,0.47576831339143399,0.12342088429061493,-1.1830581834079448,0.64582154236426259,-7.4209898970108537,-7.4209898970108519,-4.6938559778473934]
[97,5.6312473117793416E-2,0.82615584090670624,1.0246487937179096,5.796017729110519E-2,6.5681029850615937,6.5681029850615964,3.2795097648372229]
[98,0.80804733641082538,0.26781166835787318,-0.72944115693617617,1.6505064811576582,-6.1513448145968557,-6.1513448145968557,8.1002059346402842]
[99,0.49894266970018275,0.59543950981597049,0.29983206290006392,0.69103475270792181,4.1363772173852462,4.1363772173852462,2.2308740561124525]
[100,0.32081795804802316,0.15219174065625574,-1.0926718724121605,0.38686608433457653,-5.0090271908457229,-5.0090271908457229,11.000787807583098]

{"sheet":"Student t","index":26,"n_rows":103,"n_cols":8,"rows_kept":103,"cut":false,"hidden":false,"merged":[[13,4,13,6],[0,0,0,4],[4,4,4,7],[8,4,8,6],[9,4,9,6],[10,4,10,6],[11,4,11,6]]}
["UNIVARIATE STUDENT'S T"]
[]
["Observation\nNumber","Macro\nGenerated\nVariate"]
[1,{"$f":"Studentt($F$7)","v":-0.7194090397152072}]
[{"$f":"A4+1","v":2},-0.66630167294295983,null,null,"Population Parameters"]
[{"$f":"A5+1","v":3},-1.1915731011491479,null,null,"Name","Value","Type","Feasible Range"]
[4,1.6743105219069276,null,null,"k = ",7,"Shape","Any Finite Positive Integer"]
[5,-0.83598047494351868]
[6,0.17602357219006901,null,null,"Distribution Type:",null,null,"Continuous"]
[7,-1.0722257550907559,null,null,"Distrbution Name:",null,null,"Student's t"]
[8,0.40773065537943465,null,null,"Variate Number:",null,null,"Univariate"]
[9,0.1038465473102977,null,null,"Simulation Method:",null,null,"Convolution"]
[10,1.3755056750658523]
[11,9.5908751111508525E-2,null,null,"Macro Format:",null,null,"=Studentt(k)"]
[12,6.9062289376762093E-2]
[13,2.3526408476560063,null,null,null,null,"Notes:","1. The Student's t distribution does not lend"]
[14,1.1318499320783313,null,null,null,null,null,"itself easily to a manual presentation so no"]
[15,-1.8925787825566567,null,null,null,null,null,"manual example is provided here, only the"]
[16,0.29144124778658914,null,null,null,null,null,"output of the macro generated variates."]
[17,-0.80211281402256351]
[18,1.5940584767146786]
[19,-2.522426428948346]
[20,-0.10768667394595974]
[21,-0.31243321818158082]
[22,0.92675139871298085]
[23,9.4430658985316218E-2]
[24,0.15357963724702042]
[25,-1.1782802496686309]
[26,0.7538488733213663]
[27,0.20838187310171441]
[28,0.24926882391450583]
[29,0.38787671905152032]
[30,-1.4605895363825729]
[31,-0.17579852879476532]
[32,-1.730145590244708]
[33,3.3274138036899426]
[34,0.14726575222553587]
[35,-0.21495771423000115]
[36,0.80097523817605787]
[37,-1.0542635460142615]
[38,1.2108692668866252]
[39,-0.82523656643027199]
[40,0.21486796825086735]
[41,1.9096208540549788]
[42,0.904190518190647]
[43,-1.091205055559856]
[44,0.52242533462427299]
[45,0.50544180686426743]
[46,-0.12320642869488829]
[47,-0.51217012206456258]
[48,0.45247418585680638]
[49,-0.2387037873897426]
[50,0.95387717969535613]
[51,-1.8246888831363188]
[52,0.24688137098395224]
[53,-1.4861976271467878]
[54,-1.9167170106264515E-2]
[55,1.1285445110036103]
[56,-1.0287899258248403]
[57,0.37253578528826159]
[58,0.63617996495201246]
[59,-0.31263517477965269]
[60,-0.60563201300363334]
[61,-6.2270566734753729E-2]
[62,-1.6294338817943077]
[63,0.31567646706984831]
[64,-0.35503888222572227]
[65,-8.8798696591688514E-2]
[66,{"$f":"Studentt($F$7)","v":-0.31114743050331933}]
[{"$f":"A69+1","v":67},-0.34907041813692929]
[68,0.60505558795543934]
[69,-1.2776368652271435]
[70,0.78254482434284622]
[71,-1.1011555776948272E-2]
[72,2.4294127395525411]
[73,-0.78444896519147622]
[74,-1.1065819443256306]
[75,0.11555930079355806]
[76,-0.74502954933891286]
[77,-9.134417557138326E-2]
[78,-1.6422520349016838]
[79,-2.4808141541124598]
[80,-8.5699356978694977E-2]
[81,0.40254967860286794]
[82,0.42916681443312565]
[83,1.6165138504046397]
[84,0.86654230924064335]
[85,0.25265513319614885]
[86,0.16466060912980868]
[87,0.31445896167932347]
[88,-1.2043316899227328]
[89,0.22007854370700514]
[90,0.89823126696012789]
[91,-7.0745849628503304E-2]
[92,0.49676541796192708]
[93,0.34111297290263976]
[94,-0.35685314624007225]
[95,-1.275270071380729]
[96,1.8204668500150845]
[97,4.5008032647280649E-2]
[98,-0.53075382245064429]
[99,0.14028026788495515]
[100,-0.18441129722857541]

{"sheet":"Triangular","index":27,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[0,0,0,5],[4,6,4,9],[15,6,15,8],[10,6,10,8],[11,6,11,8],[12,6,12,8],[13,6,13,8]]}
["UNIVARIATE TRIANGULAR"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Triangular\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"IF($B4<($H$9-$H$7)/($H$8-$H$7),$H$7+SQRT($B4*($H$8-$H$7)*($H$9-$H$7)),$H$8-SQRT((1-$B4)*($H$8-$H$7)*($H$8-$H$9)))","v":3.1991843068803658},{"$f":"Triangular($H$7,$H$8,$H$9,$B4)","v":3.1991843068803658},{"$f":"Triangular($H$7,$H$8,$H$9)","v":3.1517881586754011}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"IF($B5<($H$9-$H$7)/($H$8-$H$7),$H$7+SQRT($B5*($H$8-$H$7)*($H$9-$H$7)),$H$8-SQRT((1-$B5)*($H$8-$H$7)*($H$8-$H$9)))","v":5.07332833248564},5.07332833248564,4.3276971858359143,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,5.2099291439922979,5.2099291439922979,5.9515944325155008,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,4.5451152827519188,4.5451152827519188,4.8350436958158971,null,"a = ",1,"Location","Any finite real number"]
[5,0.86717342695468203,5.4537534754070673,5.4537534754070673,3.8464639310389246,null,"b = ",7,"Location","Any finite real number, a<b"]
[6,0.27994300504477809,3.244765932298066,3.244765932298066,4.0539324486197135,null,"c = ",4,"Location","Any finite real number a < c < b"]
[7,0.93667220783619842,5.9323388838454267,5.9323388838454267,3.5005058730433465]
[8,0.43191155671140469,3.7882625451713268,3.7882625451713268,4.0992694475950309,null,"Distribution Type:",null,null,"Continuous"]
[9,0.96203701528155405,6.1733599786291329,6.1733599786291329,1.8157581878307312,null,"Distrbution Name:",null,null,"Triangular"]
[10,0.14240354575933512,2.6010196200134565,2.6010196200134565,1.533178978677163,null,"Variate Number:",null,null,"Univariate"]
[11,0.20171971836271319,2.9055064761183145,2.9055064761183145,4.9358805165442803,null,"Simulation Method:",null,null,"Inverse Transform"]
[12,0.58041618261550787,4.251817198052346,4.251817198052346,5.4222544758098117]
[13,0.34366851316718994,3.4871737448375852,3.4871737448375852,3.581514384697885,null,"Macro Format:",null,null,"=triangular(a, b, c, [unif])"]
[14,0.9651686825697714,6.2081895973504047,6.2081895973504047,3.8306226502667977]
[15,0.38704808829902526,3.6394820683957021,3.6394820683957021,3.2027200367246613,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[16,0.86385756571325945,5.4345723213251498,5.4345723213251498,3.90185546875,null,null,null,null,"your own uniform random variable (unif). If"]
[17,0.17476282037902591,2.7736208069433745,2.7736208069433745,5.1845322603188624,null,null,null,null,"not provided, the function will generate one"]
[18,0.38117659587117037,3.6193851808546729,3.6193851808546729,4.7828170776414449,null,null,null,null,"to be used in the formula."]
[19,0.87794506028866293,5.5177756867450638,5.5177756867450638,4.5065147167538369,null,null,null,null,"2. Column C shows the formula used in the"]
[20,0.18238019015349183,2.811861866358154,2.811861866358154,3.1435872486048444,null,null,null,null,"macro directly in the cell.  Column D generates"]
[21,0.39753335201985007,3.674995389969355,3.674995389969355,6.3312775697775976,null,null,null,null,"the random variable with the macro, using the"]
[22,0.74199757940000399,4.844995691234022,4.844995691234022,4.0803020040036655,null,null,null,null,"same uniform random variable (column A) as"]
[23,0.57082894586967958,4.2205973709543692,4.2205973709543692,2.0444721145267533,null,null,null,null,"used in Column C, and therefore the output of"]
[24,0.90195869363590486,5.6715635075195685,5.6715635075195685,5.6191370854834526,null,null,null,null,"Columns C and D will match.  Column E runs"]
[25,0.43843055863807978,3.8092258818908524,3.8092258818908524,3.1232524867014604,null,null,null,null,"the macro using an internally generated "]
[26,0.3929492390413114,3.6595274585428905,3.6595274585428905,4.8817240004616167,null,null,null,null,"uniform random input."]
[27,0.2515715048326993,3.1279772289638315,3.1279772289638315,3.6559879398100863]
[28,0.30550021398012439,3.3449954907509394,3.3449954907509394,3.0025252552797284]
[29,7.9387447484473794E-2,2.1953970280708113,2.1953970280708113,1.0882621541933688]
[30,0.82057811417206794,5.2028928955393958,5.2028928955393958,3.8440119654126099]
[31,5.0767455327721533E-3,1.3022935983276833,1.3022935983276833,3.5043981250507334]
[32,2.9980457362279278E-2,1.7346075363900284,1.7346075363900284,5.0597225223948961]
[33,0.89698739215075429,5.6382999811682373,5.6382999811682373,4.0995063568839853]
[34,4.8518018441997213E-2,1.9345182352185268,1.9345182352185268,5.2498840983488151]
[35,0.37123916516677757,3.5850154686194813,3.5850154686194813,3.427995196669225]
[36,0.18273885825049341,2.8136425911708409,2.8136425911708409,4.7664574259709518]
[37,0.12050005291704391,2.4727528484123837,2.4727528484123837,4.1535070464199482]
[38,0.64945693361731327,4.4880734097334045,4.4880734097334045,4.0665502672459635]
[39,0.84523354850406707,5.3309295620235817,5.3309295620235817,6.3581560148695253]
[40,0.96559113278394504,6.2130059657856425,6.2130059657856425,4.693041068389304]
[41,0.66499232931154673,4.5443660548868117,4.5443660548868117,5.8762185019896505]
[42,0.48716817186481609,3.9612543108565816,3.9612543108565816,5.6975360104345745]
[43,0.77210315614728597,4.9746251731225524,4.9746251731225524,6.5732525230978416]
[44,0.82636627627465631,5.232117926145472,5.232117926145472,4.2222647641048763]
[45,0.30996283637913491,3.3620607644225471,3.3620607644225471,5.5235428620645557]
[46,0.1840653161997976,2.8202130896124107,2.8202130896124107,3.5819715068790372]
[47,0.58275788798882977,4.2594967585859234,4.2594967585859234,6.0719714821766013]
[48,0.3211056530871087,3.4041426237991699,3.4041426237991699,3.8090234250062576]
[49,0.94059973373021577,5.9659764060447573,5.9659764060447573,3.1265356741845189]
[50,0.14907620621989892,2.6381000311208656,2.6381000311208656,3.9163317397230948]
[51,0.38302044178353878,3.6257128464673545,3.6257128464673545,2.3629444219938511]
[52,8.4815952479745493E-2,2.2355918195890658,2.2355918195890658,3.067651730266328]
[53,0.84221407414122895,5.3147265309576968,5.3147265309576968,4.0410352046594582]
[54,0.40498559499715014,3.699951982896863,3.699951982896863,3.3061588827602217]
[55,0.31192254229901473,3.3695159339793994,3.3695159339793994,3.5455882560612531]
[56,7.3945219604894419E-2,2.1536957800425984,2.1536957800425984,4.2902916608434261]
[57,0.41540561914582874,3.7344654220934883,3.7344654220934883,3.8831799900939266]
[58,0.94334481547755944,5.9901518324995928,5.9901518324995928,3.7964550107886792]
[59,0.6294690698059815,4.4174515021993619,4.4174515021993619,3.9893407402013454]
[60,0.21751765244325438,2.9787161858080049,2.9787161858080049,4.1889163722668492]
[61,0.81132182231923589,5.1571198632971935,5.1571198632971935,3.1329118474940785]
[62,0.47641953418452843,3.9284042779851132,3.9284042779851132,2.7062326828633263]
[63,0.92308615531225435,5.8233738043119123,5.8233738043119123,4.600464988095907]
[64,0.62241658364570296,4.392989932052938,4.392989932052938,4.1725481739657138]
[65,0.56290274788396399,4.1950489241185238,4.1950489241185238,3.238082557367405]
[66,0.27617460253729631,{"$f":"IF($B69<($H$9-$H$7)/($H$8-$H$7),$H$7+SQRT($B69*($H$8-$H$7)*($H$9-$H$7)),$H$8-SQRT((1-$B69)*($H$8-$H$7)*($H$8-$H$9)))","v":3.2296059843997846},{"$f":"Triangular($H$7,$H$8,$H$9,$B69)","v":3.2296059843997846},{"$f":"Triangular($H$7,$H$8,$H$9)","v":1.6327599397660069}]
[{"$f":"A69+1","v":67},0.98183097898545246,6.428123808624755,6.428123808624755,2.7898226792932248]
[68,0.17855864253016906,2.7927787274348841,2.7927787274348841,5.131435471109377]
[69,0.14106716857892998,2.5934895777571749,2.5934895777571749,3.7474717308999042]
[70,0.78799892820694739,5.0465365904949877,5.0465365904949877,2.431740709165759]
[71,0.62019869479720879,4.3853444789704623,4.3853444789704623,3.4785673528373127]
[72,0.32070616340267466,3.4026466534320323,3.4026466534320323,6.5312786111026604]
[73,0.71916827005391148,4.7516737027224911,4.7516737027224911,2.3915263908561992]
[74,0.70290736382840724,4.6874975781442583,4.6874975781442583,5.2046975756098757]
[75,0.154172834186179,2.6658664458326848,2.6658664458326848,3.3240910599197462]
[76,0.27977295388613965,3.2440840380766747,3.2440840380766747,2.6214295188908245]
[77,0.42321062277449939,3.7600346392646942,3.7600346392646942,2.9747680238103333]
[78,0.98136142771892321,6.4207813011828936,6.4207813011828936,6.0880144681195913]
[79,0.20085756040090119,2.9014300111274727,2.9014300111274727,4.5140630485875741]
[80,0.16133779816984994,2.7041362524919474,2.7041362524919474,3.4725690347196512]
[81,0.25863578352871763,3.1576478173040465,3.1576478173040465,5.7487816072810967]
[82,0.8347220398143228,5.2751802171408775,5.2751802171408775,4.2729204116198112]
[83,0.51591167107959424,4.0481209508912288,4.0481209508912288,5.0976193723395244]
[84,0.24633192212221666,3.1057005005935436,3.1057005005935436,2.3204898150859039]
[85,0.59063871388364364,4.285501307774414,4.285501307774414,4.2635526826013184]
[86,0.65393134749071002,4.5041563059423737,4.5041563059423737,2.2433430317371776]
[87,0.56445460206933995,4.2000326496989508,4.2000326496989508,4.6563507101715542]
[88,0.10565266639072934,2.3790387938825823,2.3790387938825823,5.9831319932761922]
[89,0.59226465879030998,4.2908975394469815,4.2908975394469815,6.4666661014162514]
[90,0.72089126375496948,4.7585814196338632,4.7585814196338632,6.2240834518354591]
[91,0.58803803186325454,4.276892321912074,4.276892321912074,2.761673615886127]
[92,0.76602838211191659,4.9478087023901747,4.9478087023901747,3.6978870866447591]
[93,0.48285856602942256,3.9481272341148381,3.9481272341148381,4.4919567036099481]
[94,0.62864718503333628,4.4145888780698836,4.4145888780698836,2.5098780581518101]
[95,0.33779794281158637,3.4658392020990654,3.4658392020990654,2.7028847971224632]
[96,0.47576831339143399,3.9264021666623012,3.9264021666623012,5.2692138067489811]
[97,5.6312473117793416E-2,2.0067892113646639,2.0067892113646639,4.9945858388081952]
[98,0.80804733641082538,5.141197174360566,5.141197174360566,2.4325647637072385]
[99,0.49894266970018275,3.9968263304040974,3.9968263304040974,4.2898561611553188]
[100,0.32081795804802316,3.4030653850580963,3.4030653850580963,1.9479757576993566]

{"sheet":"Weibull","index":28,"n_rows":103,"n_cols":10,"rows_kept":103,"cut":false,"hidden":false,"merged":[[15,6,15,8],[0,0,0,5],[4,6,4,9],[10,6,10,8],[11,6,11,8],[12,6,12,8],[13,6,13,8]]}
["UNIVARIATE WEIBULL"]
[]
["Observation\nNumber","Uniform\nRandom\nVariate","Weibull\nRandom \nVariate","Macro\nGenerated\nVariate, U(0,1)\nsubmitted","Macro\nGenerated\nVariate w/o\nU(0,1)"]
[1,0.26868953420160424,{"$f":"$H$7+$H$8*(-LN($B4))^(1/$H$9)","v":8.4241623801761953},{"$f":"Weibullrv($H$7,$H$8,$H$9,$B4)","v":8.4241623801761953},{"$f":"Weibullrv($H$7,$H$8,$H$9)","v":8.4386650562581771}]
[{"$f":"A4+1","v":2},0.79377423808874648,{"$f":"$H$7+$H$8*(-LN($B5))^(1/$H$9)","v":6.1594284063626752},6.1594284063626752,7.3699491249360651,null,"Population Parameters"]
[{"$f":"A5+1","v":3},0.82198035169288064,5.9924248691893043,5.9924248691893043,9.8361802940655103,null,"Name","Value","Type","Feasible Range"]
[4,0.66519672361232263,6.7943429086565832,6.7943429086565832,8.4385209102154057,null,"mu = ",2,"Location","Real number greater than or equal to zero"]
[5,0.86717342695468203,5.6865266543502626,5.6865266543502626,6.1902885859401975,null,"sigma = ",6,"Scale","Real number greater than zero"]
[6,0.27994300504477809,8.3734236209045729,8.3734236209045729,8.9230331995178869,null,"alpha = ",4,"Shape","Real number greater than zero"]
[7,0.93667220783619842,5.0344642212270543,5.0344642212270543,9.2912183108503683]
[8,0.43191155671140469,7.74329176950347,7.74329176950347,8.1093924633518046,null,"Distribution Type:",null,null,"Continuous"]
[9,0.96203701528155405,4.6612494763514949,4.6612494763514949,7.4308639649012704,null,"Distrbution Name:",null,null,"Weibull"]
[10,0.14240354575933512,9.0893961471057114,9.0893961471057114,8.2124000313537149,null,"Variate Number:",null,null,"Univariate"]
[11,0.20171971836271319,8.7490194404954167,8.7490194404954167,10.136933582872231,null,"Simulation Method:",null,null,"Inverse Transform"]
[12,0.58041618261550787,7.1529146188725763,7.1529146188725763,8.4155242963888366]
[13,0.34366851316718994,8.099608534265597,8.099608534265597,8.343043853025339,null,"Macro Format:",null,null,"=Weibullrv(mu, sigma, alpha, [unif])"]
[14,0.9651686825697714,4.6035303040920406,4.6035303040920406,5.7416287057203839]
[15,0.38704808829902526,7.9223136926028142,7.9223136926028142,6.5579818801590477,null,null,null,"Notes:","1.  With this function you can optionally submit"]
[16,0.86385756571325945,5.7110558217091318,5.7110558217091318,6.0184726004828422,null,null,null,null,"your own uniform random variable (unif). If"]
[17,0.17476282037902591,8.8953788920465797,8.8953788920465797,7.3621685122882123,null,null,null,null,"not provided, the function will generate one"]
[18,0.38117659587117037,7.9460145098849591,7.9460145098849591,8.056522565195559,null,null,null,null,"to be used in the formula."]
[19,0.87794506028866293,5.6039605497238822,5.6039605497238822,5.9347139260756325,null,null,null,null,"2. Column C shows the formula used in the"]
[20,0.18238019015349183,8.8528237733319273,8.8528237733319273,4.7107450701552223,null,null,null,null,"macro directly in the cell.  Column D generates"]
[21,0.39753335201985007,7.8801725671089882,7.8801725671089882,6.8955488930102078,null,null,null,null,"the random variable with the macro, using the"]
[22,0.74199757940000399,6.4345988308476558,6.4345988308476567,6.11106096000145,null,null,null,null,"same uniform random variable (column A) as"]
[23,0.57082894586967958,7.1919110602664871,7.1919110602664871,6.1033554717234733,null,null,null,null,"used in Column C, and therefore the output of"]
[24,0.90195869363590486,5.4006115678484647,5.4006115678484647,7.8081007457412479,null,null,null,null,"Columns C and D will match.  Column E runs"]
[25,0.43843055863807978,7.7174977864094174,7.7174977864094174,7.2208982640967605,null,null,null,null,"the macro using an internally generated "]
[26,0.3929492390413114,7.8985690634372467,7.8985690634372467,8.8970942036061764,null,null,null,null,"uniform random input."]
[27,0.2515715048326993,8.5031418353380275,8.5031418353380275,5.5169361884541477]
[28,0.30550021398012439,8.26115638607439,8.26115638607439,8.3132228888433737]
[29,7.9387447484473794E-2,9.569685488410709,9.569685488410709,7.8101021911359565]
[30,0.82057811417206794,6.0010895396173165,6.0010895396173165,10.561761358819151]
[31,5.0767455327721533E-3,11.096475353740248,11.096475353740248,5.7930905959319814]
[32,2.9980457362279278E-2,10.210917311215521,10.210917311215521,7.4546034195369106]
[33,0.89698739215075429,5.4452607183656507,5.4452607183656507,6.4618492002426553]
[34,4.8518018441997213E-2,9.9133800534103678,9.9133800534103678,6.2242693608175266]
[35,0.37123916516677757,7.9863164220938634,7.9863164220938634,4.0771904130091681]
[36,0.18273885825049341,8.850844923539178,8.850844923539178,5.9520476191184439]
[37,0.12050005291704391,9.2366165018796202,9.2366165018796202,6.7868813589634733]
[38,0.64945693361731327,6.8632469888424064,6.8632469888424064,5.6551515487583872]
[39,0.84523354850406707,5.8421162140802707,5.8421162140802707,9.7412826907990517]
[40,0.96559113278394504,4.5954587991918565,4.5954587991918565,4.7506912588095052]
[41,0.66499232931154673,6.7952461845291054,6.7952461845291054,8.92014529893099]
[42,0.48716817186481609,7.5252953978820516,7.5252953978820507,6.8493307257785592]
[43,0.77210315614728597,6.2788194627939138,6.2788194627939138,5.6367236964475733]
[44,0.82636627627465631,5.9650502793488371,5.9650502793488371,5.7610940844709759]
[45,0.30996283637913491,8.2419250902376042,8.2419250902376042,9.5694742709824716]
[46,0.1840653161997976,8.8435453434363769,8.8435453434363769,7.3435441206941103]
[47,0.58275788798882977,7.1433534007043651,7.1433534007043651,7.961281715030764]
[48,0.3211056530871087,8.1943309707681475,8.1943309707681475,6.9659095001159317]
[49,0.94059973373021577,4.9847349952154421,4.9847349952154421,8.6366669259308129]
[50,0.14907620621989892,9.0473838745237405,9.0473838745237405,9.4926688157751933]
[51,0.38302044178353878,7.9385631819416957,7.9385631819416957,7.9405350904428609]
[52,8.4815952479745493E-2,9.5197861793103531,9.5197861793103531,8.4229704401791921]
[53,0.84221407414122895,5.862398996917463,5.862398996917463,7.6836735830186198]
[54,0.40498559499715014,7.8503493579377164,7.8503493579377164,7.4180947507690727]
[55,0.31192254229901473,8.2335115354283257,8.2335115354283257,9.7934360999384946]
[56,7.3945219604894419E-2,9.622184437103467,9.622184437103467,7.7573945242948161]
[57,0.41540561914582874,7.8088033222419817,7.8088033222419817,5.7952973002649832]
[58,0.94334481547755944,4.9485735706674099,4.9485735706674099,6.8294789582316096]
[59,0.6294690698059815,6.9490064176319715,6.9490064176319715,7.3917871466010094]
[60,0.21751765244325438,8.6681067422586597,8.6681067422586597,7.1552352549572511]
[61,0.81132182231923589,6.0572784692911359,6.0572784692911359,8.506690934643645]
[62,0.47641953418452843,7.5676594130375934,7.5676594130375934,8.9064021876975623]
[63,0.92308615531225435,5.191303627375472,5.1913036273754711,8.1418658360386722]
[64,0.62241658364570296,6.9788517588900278,6.9788517588900278,8.143975028938172]
[65,0.56290274788396399,7.223983562726799,7.223983562726799,6.263141753831535]
[66,0.27617460253729631,{"$f":"$H$7+$H$8*(-LN($B69))^(1/$H$9)","v":8.3903174292817955},{"$f":"Weibullrv($H$7,$H$8,$H$9,$B69)","v":8.3903174292817955},{"$f":"Weibullrv($H$7,$H$8,$H$9)","v":8.229690519555545}]
[{"$f":"A69+1","v":67},0.98183097898545246,4.2078929860673933,4.2078929860673933,5.3651710158828863]
[68,0.17855864253016906,8.8740450447816563,8.8740450447816563,5.4243529025908632]
[69,0.14106716857892998,9.0979543978527904,9.0979543978527904,7.1696651785808303]
[70,0.78799892820694739,6.1919237433400021,6.1919237433400021,8.883532906813663]
[71,0.62019869479720879,6.9881965258180703,6.9881965258180703,10.677067466238181]
[72,0.32070616340267466,8.1960273045392178,8.1960273045392178,7.2333849334793863]
[73,0.71916827005391148,6.546401496855788,6.5464014968557871,7.114120604961605]
[74,0.70290736382840724,6.623281342265269,6.623281342265269,9.8245058810341259]
[75,0.154172834186179,9.0160573348160984,9.0160573348160984,6.5871062629422887]
[76,0.27977295388613965,8.374183931172503,8.374183931172503,7.598919890557216]
[77,0.42321062277449939,7.777785055629951,7.777785055629951,6.3003385923582158]
[78,0.98136142771892321,4.2221541707341936,4.2221541707341936,7.6370524615015771]
[79,0.20085756040090119,8.7535292265340523,8.7535292265340523,6.8471406485353548]
[80,0.16133779816984994,8.9730476975468321,8.9730476975468321,7.1986522631104686]
[81,0.25863578352871763,8.4702681268791409,8.4702681268791409,9.8123193657644912]
[82,0.8347220398143228,5.9116919472393796,5.9116919472393796,9.5553737816835156]
[83,0.51591167107959424,7.4117306669943455,7.4117306669943455,7.9077019684065002]
[84,0.24633192212221666,8.5277967758299482,8.5277967758299482,6.9864414103060941]
[85,0.59063871388364364,7.1110639125013213,7.1110639125013213,5.809756529063308]
[86,0.65393134749071002,6.8437903780762266,6.8437903780762266,10.804378942818129]
[87,0.56445460206933995,7.2177153905342104,7.2177153905342104,7.400070125553186]
[88,0.10565266639072934,9.3465074608486418,9.3465074608486418,7.1776236866642575]
[89,0.59226465879030998,7.1043797046994337,7.1043797046994328,4.6361285038107329]
[90,0.72089126375496948,6.5381285413767518,6.5381285413767509,7.7413705636672985]
[91,0.58803803186325454,7.1217390610827618,7.1217390610827618,6.3977855013486309]
[92,0.76602838211191659,6.3111213021953194,6.3111213021953194,8.5868156386684298]
[93,0.48285856602942256,7.5422841981350643,7.5422841981350643,6.0604471286596713]
[94,0.62864718503333628,6.9524950242177113,6.9524950242177113,5.3639395920944208]
[95,0.33779794281158637,8.1240600123380418,8.1240600123380418,7.9843612147051637]
[96,0.47576831339143399,7.5702254475308361,7.5702254475308361,7.0868039807361374]
[97,5.6312473117793416E-2,9.8141212920574752,9.8141212920574752,7.5433889382224439]
[98,0.80804733641082538,6.076756375529996,6.076756375529996,7.9260175035329059]
[99,0.49894266970018275,7.4788410190211501,7.4788410190211501,9.0506616645944451]
[100,0.32081795804802316,8.1955525239320206,8.1955525239320206,8.9110751434710096]